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Dissertations / Theses on the topic 'Programming (mathematics)'

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Published: 4 June 2021
Last updated: 29 July 2024

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1

Rolandsson, Jakob. "Programming as Mathematics – A Curriculum Perspective." Thesis, Uppsala universitet, Matematiska institutionen, 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-451806.

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2

Yung, Simon Yun Pui. "Definitive programming : a paradigm for exploratory programming." Thesis, University of Warwick, 1992. http://wrap.warwick.ac.uk/78859/.

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Exploratory software development is a method that applies to the development of programs whose requirement is initially unclear. In such a context, it is only through prototyping and experimenting on the prototypes that the requirement can be fully developed. A good exploratory software development method must have a short development cycle. This thesis describes our attempt to fulfil this demand. We address this issue in the programming language level. A novel programming paradigm - definitive (definition-based) programming - is developed. In definitive programming, a state is represented by a set of definitions (a definitive script) and a state transition is represented by a redefinition. By means of a definition, a variable is defined either by an explicit value or by a formula in terms of other variables. Unless this variable is redefined, the relationship between the variables within the definition persists. To apply this state representation principle, we have developed some definitive notations in which the underlying algebras used in formulating definitions are domain specific. We have also developed an agent-oriented specification language by which we can model state transitions over definitive scripts. The modelling principles of definitive programming rest on a solid foundation in observation and experiment that is essential for exploratory software development. This thesis describes how we may combine definitive notations and the agent oriented programming concept to produce software tools that are useful in exploratory software development. In this way, definitive programming can be considered as a paradigm for exploratory programming.
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Sharifi, Mokhtarian Faranak. "Mathematical programming with LFS functions." Thesis, McGill University, 1992. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=56762.

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Differentiable functions with a locally flat surface (LFS) have been recently introduced and studied in convex optimization. Here we extend this motion in two directions: to non-smooth convex and smooth generalized convex functions. An important feature of these functions is that the Karush-Kuhn-Tucker condition is both necessary and sufficient for optimality. Then we use the properties of linear LFS functions and basic point-to-set topology to study the "inverse" programming problem. In this problem, a feasible, but nonoptimal, point is made optimal by stable perturbations of the parameters. The results are applied to a case study in optimal production planning.
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4

Fuentes, Martinez Ana. "Teachers’ tactics when programming and mathematics converge." Licentiate thesis, Högskolan Väst, Avd för medier och design, 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:hv:diva-16379.

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Teachers’ everyday practices are embedded in school contexts in which their teaching autonomy is constrained by rules, moral obligations, physical settings,and official directives. When a curricular revision mandated that programming was to be a part of mathematics in upper secondary education, teachers’ conditions changed. How teachers adapted to the new curriculum and how they navigated the tensions and contradictions that they encountered is in this thesis analyzed in terms of teachers’ tactics and policy strategies. The overall goal of the investigation is to contribute to a critical understanding of how mathematics teachers integrate programming in their professional practice and how this integration aligns and diverges from the intentions behind the reform. The empirical material is drawn from nine individual interviews with mathematics teachers that were already proficient in programming. The teachers’ unit plans and other lesson materials featuring programming activities served as a trigger point to delve into further reflections upon their own professional practices. To complete the scene, the policy documents were also examined. These included the mathematics curriculum, as well as related official documents and a collection of institutionally sanctioned programming exercises and demonstrations. Two tactical approaches were made apparent when mathematics teachers began to integrate computer programming in their subject: Dual teaching and Interspersed programming. The teacher’s use of dual teaching practices or interspersed programming are tactics shaped by and in response to the conditions of the new curriculum and their own preferences and views on student learning. These two tactics disclose different ontological commitments in relation to the strategies dictated by the curriculum and reflect a cardinal distinction between planning mathematics activities with elements of programming and planning programming activities with elements of mathematics. Of relevance for teachers and curriculum designers is the understanding of (a) how the notion of programming and mathematics as separate subjects oversimplifies teachers’ actual integration practices, and (b) how the curricular choices made by policy can shape the teaching tactics adopted by educators.
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Davidescu, Diana Maria. "Convexifiable smooth programming and applications." Thesis, McGill University, 2004. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=82216.

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This thesis is an introduction to the study of convexification problems involving smooth functions in the area of continuous mathematical programming. The results are applied to a real life problem in oil production. An improved model is formulated for the company which yields environmentally friendlier optimal solutions at the same profit level.
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6

Reeves, Laurence H. "Mathematical Programming Applications in Agroforestry Planning." DigitalCommons@USU, 1991. https://digitalcommons.usu.edu/etd/6495.

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Agroforestry as a sustainable production system has been recognized as a land use system with the potential to slow encroachment of agriculture onto forested lands in developing countries. However, the acceptance of nontraditional agroforestry systems has been hampered in some areas due to the risk-averse nature of rural agriculturalists. By explicitly recognizing risk in agroforestry planning, a wider acceptance of agroforestry is possible. This thesis consists of a collection of three papers that explore the potential of modern stock portfolio theory to reduce financial risk in agroforestry planning. The first paper presents a theoretical framework that incorporates modern stock portfolio theory through mathematical programming. This framework allows for the explicit recognition of financial risk by using a knowledge of past net revenue trends and fluctuations for various cropping systems, with the assumption that past trend behavior is indicative of future behavior. The paper demonstrates how financial risk can be reduced by selecting cropping systems with stable and/or negatively correlated net revenues, thereby reducing the variance of future net revenues. Agroforestry systems generally entail growing simultaneously some combination of plant and/or animal species. As a result, interactions between crops usually cause crop yields within systems to deviate from what would be observed under monocultural conditions, thus requiring some means of incorporating these interactions into mathematical models. The second paper presents two approaches to modeling such interactions, depending on the nature of the interaction. The continuous system approach is appropriate under conditions where yield interactions are linear between crops and allows for a continuous range of crop mixtures. The discrete system approach should be used where nonlinear interactions occur. Under this second approach, decision variables are defined as fixed crop mixtures with known yields. In the third paper, the techniques presented above were applied to a case study site in Costa Rica. Using MOTAD programming and a discrete system approach, a set of minimum-risk farm plans were derived for a hypothetical farm. For the region studied, results indicate that reductions in risk require substantial reductions in expected net revenue.
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7

Esche, Alexander. "Mathematical Programming and Magic| The Gathering(RTM)." Thesis, Northern Illinois University, 2018. http://pqdtopen.proquest.com/#viewpdf?dispub=10689404.

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In this paper mathematical programming techniques were used to determine the optimal strategy for playing Magic: The Gathering®. Games with the cards Lightning Bolt, Mountain, and Vexing Devil were evaluated using the minimax algorithm to determine the winner when all information about the cards is assumed known to both players. Computation time was shortened through the use of an evaluation function, a random forest algorithm that had been trained on 1000 completed games. A winning percentage was established for each pair of decks where the number of creatures was less than eight. Using linear programming, the optimal mixed strategy was then calculated. By repeating the simulations, a standard deviation for the winning percentages was estimated. Techniques from robust optimization were then used to determine the optimal strategy under different possible variations. Last, an imperfect information player was constructed that made choices based on guessing the order of the cards in its deck and the composition of the opponent's deck, playing through the perfect information games of these guesses, and making the choice that won in most of these simulations. With decks of eight or fewer creatures, this imperfect information player played below or near a player who used an aggressive heuristic. When the number of possible creatures was increased to 16, the imperfect information player's performance was better than the aggressive heuristic.

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8

Cregger, Michael L. "The general mixed-integer linear programming problem an empirical analysis /." Instructions for remote access. Click here to access this electronic resource. Access available to Kutztown University faculty, staff, and students only, 1993. http://www.kutztown.edu/library/services/remote_access.asp.

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9

Trujillo-Cortez, Refugio. "LFS functions in stable bilevel programming." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1997. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp01/MQ37171.pdf.

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Trujillo-Cortez, Refugio. "Stable convex parametric programming and applications." Thesis, McGill University, 2000. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=37856.

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This thesis is a study of stable perturbations in convex programming models. Stability of a general model is introduced as lower semicontinuity of the feasible set mapping. This stability is shown to be equivalent to the Robinson notion of stability and regularity. In the convex case, it is also equivalent to the full-rank Slater condition. Then, the relationships between various point-to-set mappings are studied for convex models and new implications between these mappings are established. Also, local and global optimality of parameters is studied. A new result here is a characterization of locally optimal parameters that does not require stable perturbations. This result is valid, in particular, for convex models with LFS constraints. The value of the model can be improved by one of several new formulations of the marginal value formula.
The results on stability are applied for bilevel convex models and an algorithm for solving these models, based on a marginal value formula, is suggested and then applied to a real-life problem in the petroleum industry.
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11

Sundbom, Tobias. "Mathematical programming based approaches in credit scoring." Thesis, Uppsala University, Department of Mathematics, 2007. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-120980.

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12

Moor, Oege de. "Categories, relations and dynamic programming." Thesis, University of Oxford, 1991. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.305600.

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Nahum, Carole. "Second order sensitivity analysis in mathematical programming." Thesis, McGill University, 1989. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=74349.

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We consider a nonlinear mathematical program, with twice continuously differentiable functions.
If a point x$ sb0$ does not satisfy a certain Second Order Sufficient Condition (SOS) for optimality (that does not require any constraint qualification, see, e.g., BEN-ISRAEL, BEN-TAL and ZLOBEC (81)), then we prove that the knowledge of the second order properties (derivative, Hessian) of the functions is not enough to conclude that the point is optimal.
When the functions are continuously perturbed, what is the local behavior of an optimal solution x$ sb0$ and of the associate optimal value? The stability and sensitivity of the mathematical model are addressed. We present a new method for solving this problem. Our approach does not rely on the classical Lagrangian coefficients (which cannot be always defined) but rather on power series expansions because we use the primal formulations of optimality.
In the regular case, when Strict complementarity slackness holds, we recover Fiacco's results (FIACCO (83)). On the other hand, when Strict complementarity slackness does not hold, we extensively generalize Shapiro's Theorems (SHAPIRO (85)) since we do not assume Robinson's second order condition (ROBINSON (80)) but the SOS condition.
In the non-regular case, no general algorithm for computing the derivative of the optimizing point with respect to the parameters had been presented up to now.
The approach is extended to analyze the evolution of the set of Pareto minima of a multiobjective nonlinear program. In particular, we define the derivative of a point-to-set map. Our notion seems more adequate than the contingent derivative (AUBIN (81)), though the latter can easily be deduced from the former. This allows to get information about the sensitivity of the set of Pareto minima. A real-life example shows the usefulness and the simplicity of our results. Also, an application of our method to industry planning (within a general framework of Input Optimization) is made in the ideal case of a linear model.
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He, Fang. "Effective integrations of constraint programming, integer programming and local search for two combinatorial optimisation problems." Thesis, University of Nottingham, 2012. http://eprints.nottingham.ac.uk/14208/.

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This thesis focuses on the construction of effective and efficient hybrid methods based on the integrations of Constraint Programming (CP), Integer Programming (IP) and local search (LS) to tackle two combinatorial optimisation problems from different application areas: the nurse rostering problems and the portfolio selection problems. The principle of designing hybrid methods in this thesis can be described as: for the combinatorial problems to be solved, the properties of the problems are investigated firstly and the problems are decomposed accordingly in certain ways; then the suitable solution techniques are integrated to solve the problem based on the properties of substructures/subproblems by taking the advantage of each technique. For the over-constrained nurse rostering problems with a large set of complex constraints, the problems are first decomposed by constraint. That is, only certain selected set of constraints is considered to generate feasible solutions at the first stage. Then the rest of constraints are tackled by a second stage local search method. Therefore, the hybrid methods based on this constraint decomposition can be represented by a two-stage framework “feasible solution + improvement”. Two integration methods are proposed and investigated under this framework. In the first integration method, namely a hybrid CP with Variable Neighourhood Search (VNS) approach, the generation of feasible initial solutions relies on the CP while the improvement of initial solutions is gained by a simple VNS in the second stage. In the second integration method, namely a constraint-directed local search, the local search is enhanced by using the information of constraints. The experimental results demonstrate the effectiveness of these hybrid approaches. Based on another decomposition method, Dantzig-Wolfe decomposition, in the third integration method, a CP based column generation, integrates the feasibility reasoning of CP with the relaxation and optimality reasoning of Linear Programming. The experimental results demonstrate the effectiveness of the methods as well as the knowledge of the quality of the solution. For the portfolio selection problems, two integration methods, which integrate Branch-and-Bound algorithm with heuristic search, are proposed and investigated. In layered Branch-and-Bound algorithm, the problem is decomposed into the subsets of variables which are considered at certain layers in the search tree according to their different features. Node selection heuristics, and branching rules, etc. are tailored to the individual layers, which speed up the search to the optimal solution in a given time limit. In local search branching Branch-and-Bound algorithm, the idea of local search is applied as the branching rule of Branch-and-Bound. The local search branching is applied to generate a sequence of subproblems. The procedure for solving these subproblems is accelerated by means of the solution information reusing. This close integration between local search and Branch-and-Bound improves the efficiency of the Branch-and-Bound algorithm according to the experimental results. The hybrid approaches benefit from each component which is selected according to the properties of the decomposed problems. The effectiveness and efficiency of all the hybrid approaches to the two application problems developed in this thesis are demonstrated. The idea of designing appropriate components in hybrid approach concerning properties of subproblems is a promising methodology with extensive potential applications in other real-world combinatorial optimisation problems.
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15

Kaluzny, Bohdan Lubomyr. "Linear programming : pivoting on polyhedra and arrangements." Thesis, McGill University, 2005. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=100633.

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Linear programming is perhaps the most useful tool in optimization, much of it's success owed to the efficiency of the simplex method in practice --- its ability to solve problems with millions of variables with relative ease. However, whether there exists a strongly polynomial algorithm to solve linear programming remains an open question. Pivot methods, including the simplex method, remain the best hope for finding such an algorithm, despite the fact that almost all variants have been shown to require exponential time on special instances. Fundamental questions about the path length (number of iterations) of pivot methods remain unanswered. Some, such as the related Hirsch Conjecture, are famous long-standing problems in polyhedral theory. How long can a pivot path be? How many distinct degenerate solutions (bases) can appear during a simplex method cycle? How long can a finite pivot rule stall without improving the solution? Can we enumerate all possible pivot paths to optimality? Can we compute monotone disjoint pivot paths? These are some of the questions we tackle in this thesis in a quest to better understand pivot methods.
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Galup, Luis Enrique. "A programming approach to ergodic maximal inequalities /." The Ohio State University, 1997. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487944660931622.

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17

Zhou, Fangjun. "Nonmonotone methods in optimization and DC optimization of location problems." Diss., Georgia Institute of Technology, 1997. http://hdl.handle.net/1853/21777.

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18

Zhou, Xiaojie. "Characterizations of optimality in multi-objective programming." Thesis, McGill University, 1992. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=61040.

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This thesis contains several contributions to the theory of optimality conditions in single- and multi-objective optimization. The main result provides an answer to the following, apparently open, question in mathematical welfare economics: Given a feasible decision, find a saddle-point condition which is both necessary and sufficient that the decision is Pareto optimal for convex objectives and convex constraints. This result is then extended to convex multi-objective parametric optimization and to a large class of nonconvex multi-objective programs.
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19

Loucopoulos, Constantine. "Mathematical Programming Approaches to the Three-Group Classification Problem." Thesis, University of North Texas, 1993. https://digital.library.unt.edu/ark:/67531/metadc279363/.

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In the last twelve years there has been considerable research interest in mathematical programming approaches to the statistical classification problem, primarily because they are not based on the assumptions of the parametric methods (Fisher's linear discriminant function, Smith's quadratic discriminant function) for optimality. This dissertation focuses on the development of mathematical programming models for the three-group classification problem and examines the computational efficiency and classificatory performance of proposed and existing models. The classificatory performance of these models is compared with that of Fisher's linear discriminant function and Smith's quadratic discriminant function. Additionally, this dissertation investigates theoretical characteristics of mathematical programming models for the classification problem with three or more groups. A computationally efficient model for the three-group classification problem is developed. This model minimizes directly the number of misclassifications in the training sample. Furthermore, the classificatory performance of the proposed model is enhanced by the introduction of a two-phase algorithm. The same algorithm can be used to improve the classificatory performance of any interval-based mathematical programming model for the classification problem with three or more groups. A modification to improve the computational efficiency of an existing model is also proposed. In addition, a multiple-group extension of a mathematical programming model for the two-group classification problem is introduced. A simulation study on classificatory performance reveals that the proposed models yield lower misclassification rates than Fisher's linear discriminant function and Smith's quadratic discriminant function under certain data configurations. Data configurations, where the parametric methods outperform the proposed models, are also identified. A number of theoretical characteristics of mathematical programming models for the classification problem are identified. These include conditions for the existence of feasible solutions, as well as conditions for the avoidance of degenerate solutions. Additionally, conditions are identified that guarantee the classificatory non-inferiority of one model over another in the training sample.
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20

Borg, Andreas. "Designing for the incorporation of programming in mathematical education : Programming as an instrument for mathematical problem solving." Licentiate thesis, Karlstads universitet, Institutionen för pedagogiska studier (from 2013), 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:kau:diva-85625.

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This study explored Swedish upper secondary school students’ use of programming for mathematical purposes. The aim of the study was to investigate the process through which students learn how to use a programming environment as a technical artefact during mathematical problem solving and how the orchestration of such learning situations could facilitate this process. In order to study the students’ use of the programming environment, design-based research was used as the main methodological approach. The design involved the development of specific mathematical tasks to be tried out with students, as well as the orchestration of the learning situation within the classroom e.g., by preparing scaffolding to be offered to the students. The subsequent implementation of the design was analysed so that, in accordance with the cyclic approach of design-based research, it could be revised ahead of the following design cycle. The study involved two complete design cycles. In the study, the Instrumental Approach was used as the theoretical framework and the instrumental genesis of the students in using a programming environment for mathematical purposes was thus of special interest. In order to analyse this process and the associated mental schemes developed by the students, Vergnaud’s concept of scheme served as an analytical framework. The findings revealed how the students, despite having basic knowledge in programming, experienced several difficulties when trying to use the programming environment as a technical mathematical artefact. These difficulties were related both to the fact that the mathematical affordances offered by the programming environment were unclear to many of the students, as well as to the handling of more specific computational concepts such as nested loops. The findings also revealed that the transformation of mathematical notations and ideas into programming code caused students difficulties.
This study explored Swedish upper secondary school students’ use of programming for mathematical purposes. The aim of the study was to investigate the process through which students learn how to use a programming environment as a technical artefact during mathematical problem solving and how the orchestration of such learning situations could facilitate this process. In order to study the students’ use of the programming environment, design-based research was used as the main methodological approach and the Instrumental Approach served as the theoretical framework. The design involved the development of mathematical tasks to be tried out with students, as well as the orchestration of the learning situation within the classroom. The findings revealed how the students experienced several difficulties when trying to use the programming environment as a technical mathematical artefact. These difficulties were related to the fact that the mathematical affordances offered by the programming environment initially were unclear to many of the students, as well as to the handling of more specific computational concepts such as nested loops. The findings also revealed that the transformation of mathematical notations and ideas into programming code caused students difficulties.
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21

Wei, Hua. "Numerical Stability in Linear Programming and Semidefinite Programming." Thesis, University of Waterloo, 2006. http://hdl.handle.net/10012/2922.

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We study numerical stability for interior-point methods applied to Linear Programming, LP, and Semidefinite Programming, SDP. We analyze the difficulties inherent in current methods and present robust algorithms.

We start with the error bound analysis of the search directions for the normal equation approach for LP. Our error analysis explains the surprising fact that the ill-conditioning is not a significant problem for the normal equation system. We also explain why most of the popular LP solvers have a default stop tolerance of only 10-8 when the machine precision on a 32-bit computer is approximately 10-16.

We then propose a simple alternative approach for the normal equation based interior-point method. This approach has better numerical stability than the normal equation based method. Although, our approach is not competitive in terms of CPU time for the NETLIB problem set, we do obtain higher accuracy. In addition, we obtain significantly smaller CPU times compared to the normal equation based direct solver, when we solve well-conditioned, huge, and sparse problems by using our iterative based linear solver. Additional techniques discussed are: crossover; purification step; and no backtracking.

Finally, we present an algorithm to construct SDP problem instances with prescribed strict complementarity gaps. We then introduce two measures of strict complementarity gaps. We empirically show that: (i) these measures can be evaluated accurately; (ii) the size of the strict complementarity gaps correlate well with the number of iteration for the SDPT3 solver, as well as with the local asymptotic convergence rate; and (iii) large strict complementarity gaps, coupled with the failure of Slater's condition, correlate well with loss of accuracy in the solutions. In addition, the numerical tests show that there is no correlation between the strict complementarity gaps and the geometrical measure used in [31], or with Renegar's condition number.
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Steffy, Daniel E. "Topics in exact precision mathematical programming." Diss., Georgia Institute of Technology, 2011. http://hdl.handle.net/1853/39639.

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The focus of this dissertation is the advancement of theory and computation related to exact precision mathematical programming. Optimization software based on floating-point arithmetic can return suboptimal or incorrect resulting because of round-off errors or the use of numerical tolerances. Exact or correct results are necessary for some applications. Implementing software entirely in rational arithmetic can be prohibitively slow. A viable alternative is the use of hybrid methods that use fast numerical computation to obtain approximate results that are then verified or corrected with safe or exact computation. We study fast methods for sparse exact rational linear algebra, which arises as a bottleneck when solving linear programming problems exactly. Output sensitive methods for exact linear algebra are studied. Finally, a new method for computing valid linear programming bounds is introduced and proven effective as a subroutine for solving mixed-integer linear programming problems exactly. Extensive computational results are presented for each topic.
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Leong, Fu Fai. "Application of linear programming in Sudoku." Thesis, University of Macau, 2006. http://umaclib3.umac.mo/record=b1636813.

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Pudwill, Rodger A. "An investigation of an exterior point method for linear programming." Diss., Georgia Institute of Technology, 1993. http://hdl.handle.net/1853/24506.

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Silva, Robert A. "Optimizing multi-ship, multi-mission operational planning for the Joint Force Maritime Component Commander." Thesis, Monterey, Calif. : Naval Postgraduate School, 2009. http://edocs.nps.edu/npspubs/scholarly/theses/2009/Mar/09Mar%5FSilva.pdf.

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Thesis (M.S. in Operations Research)--Naval Postgraduate School, March 2009.
Thesis Advisor(s): Carlyle, W. Matthew. "March 2009." Description based on title screen as viewed on April 24, 2009. Author(s) subject terms: Integer Programming, Operational Planning, Navy Mission Planner, Navy Asset-Mission Pairing, Maritime Headquarters, Maritime Operations Center, Constrained Enumeration, Stack-based Enumeration, Mathematical Programming, Optimization, Decision Aid, Planning Tool, Ship Employment Schedule. Includes bibliographical references (p. 61-62). Also available in print.
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Hewitt, Michael R. "Integer programming based search." Diss., Atlanta, Ga. : Georgia Institute of Technology, 2009. http://hdl.handle.net/1853/31641.

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Thesis (Ph.D)--Industrial and Systems Engineering, Georgia Institute of Technology, 2010.
Committee Chair: Erera, Martin; Committee Chair: Nemhauser, George; Committee Chair: Savelsbergh, Martin; Committee Member: Ergun, Ozlem; Committee Member: Ferguson, Mark. Part of the SMARTech Electronic Thesis and Dissertation Collection.
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Easton, Kelly King. "Using integer programming and constraint programming to solve sports scheduling problems." Diss., Georgia Institute of Technology, 2002. http://hdl.handle.net/1853/25795.

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Szularz, Marek. "Quadratic programming with constant norm with parallel applications." Thesis, Kingston University, 1991. http://eprints.kingston.ac.uk/20556/.

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This thesis is concerned with the problem of minimizing a quadratic function defined on an ellipsoid, and subject to the set of linear inequality constraints. An original method is proposed, a method which generates the descent flow on the spiral, the curve on the surface of the constraining ellipsoid, characterized locally by the steepest descent of the objective function. The spiral is constructed discretely in a number of points which are the solutions of the sequence of certain artificially constrained subproblems. The properties of the spiral are studied extensively to show that the associated descent flow can be divided into three categories of the regular, separated and multiple descent flow. Particular attention is devoted to the case of the separated descent flow, which involves the discontinuity of the spiral and may pose certain difficulties in the search for the solution. The important and the original part of the thesis is also the issue of all local minima of the equality constrained version of the problem. The identification of all such minima is vital to the main problem and the corresponding method. The method which may find many practical applications, has been inspired by the opportunities given by a massively parallel computer, namely the Distributed Array Processor, although the method can find the applications in other parallel environments. The algorithm has been implemented in DAP Fortran-Plus, and a series of numerical examples is presented, some of them of practical importance in structural engineering.
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Rubalcaba, Roberto Ramon Johnson Peter D. "Fractional domination, fractional packings, and fractional isomorphisms of graphs." Auburn, Ala., 2005. http://repo.lib.auburn.edu/EtdRoot/2005/SPRING/Mathematics/Dissertation/RUBALCABA_ROBERT_56.pdf.

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Staats, Kai. "Genetic programming applied to RFI mitigation in radio astronomy." Master's thesis, University of Cape Town, 2016. http://hdl.handle.net/11427/23703.

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Genetic Programming is a type of machine learning that employs a stochastic search of a solutions space, genetic operators, a fitness function, and multiple generations of evolved programs to resolve a user-defined task, such as the classification of data. At the time of this research, the application of machine learning to radio astronomy was relatively new, with a limited number of publications on the subject. Genetic Programming had never been applied, and as such, was a novel approach to this challenging arena. Foundational to this body of research, the application Karoo GP was developed in the programming language Python following the fundamentals of tree-based Genetic Programming described in "A Field Guide to Genetic Programming" by Poli, et al. Karoo GP was tasked with the classification of data points as signal or radio frequency interference (RFI) generated by instruments and machinery which makes challenging astronomers' ability to discern the desired targets. The training data was derived from the output of an observation run of the KAT-7 radio telescope array built by the South African Square Kilometre Array (SKA-SA). Karoo GP, kNN, and SVM were comparatively employed, the outcome of which provided noteworthy correlations between input parameters, the complexity of the evolved hypotheses, and performance of raw data versus engineered features. This dissertation includes description of novel approaches to GP, such as upper and lower limits to the size of syntax trees, an auto-scaling multiclass classifier, and a Numpy array element manager. In addition to the research conducted at the SKA-SA, it is described how Karoo GP was applied to fine-tuning parameters of a weather prediction model at the South African Astronomical Observatory (SAAO), to glitch classification at the Laser Interferometer Gravitational-wave Observatory (LIGO), and to astro-particle physics at The Ohio State University.
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31

Benson, Carol Trinko Plantholt Michael. "Effect of computer instruction in finite mathematics on student achievement and attitude." Normal, Ill. Illinois State University, 1989. http://wwwlib.umi.com/cr/ilstu/fullcit?p9004078.

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Thesis (D.A.)--Illinois State University, 1989.
Title from title page screen, viewed October 14, 2005. Dissertation Committee: Michael J. Plantholt (chair), John A. Dossey, Patricia H. Klass, James T. Parr, Lawrence E. Spence. Includes bibliographical references (leaves 87-89) and abstract. Also available in print.
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32

Hearnes, Warren E. II. "Near-optimal intelligent control for continuous set-point regulator problems via approximate dynamic programming." Diss., Georgia Institute of Technology, 1999. http://hdl.handle.net/1853/24882.

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33

Wang, Xianzhi. "Resolution of Ties in Parametric Quadratic Programming." Thesis, University of Waterloo, 2004. http://hdl.handle.net/10012/1199.

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We consider the convex parametric quadratic programming problem when the end of the parametric interval is caused by a multiplicity of possibilities ("ties"). In such cases, there is no clear way for the proper active set to be determined for the parametric analysis to continue. In this thesis, we show that the proper active set may be determined in general by solving a certain non-parametric quadratic programming problem. We simplify the parametric quadratic programming problem with a parameter both in the linear part of the objective function and in the right-hand side of the constraints to a quadratic programming without a parameter. We break the analysis into three parts. We first study the parametric quadratic programming problem with a parameter only in the linear part of the objective function, and then a parameter only in the right-hand side of the constraints. Each of these special cases is transformed into a quadratic programming problem having no parameters. A similar approach is then applied to the parametric quadratic programming problem having a parameter both in the linear part of the objective function and in the right-hand side of the constraints.
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34

Violin, Alessia. "Mathematical programming approaches to pricing problems." Doctoral thesis, Universite Libre de Bruxelles, 2014. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/209173.

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There are many real cases where a company needs to determine the price of its products so as to maximise its revenue or profit.

To do so, the company must consider customers' reactions to these prices, as they may refuse to buy a given product or service if its price is too high. This is commonly known in literature as a pricing problem.

This class of problems, which is typically bilevel, was first studied in the 1990s and is NP-hard, although polynomial algorithms do exist for some particular cases. Many questions are still open on this subject.

The aim of this thesis is to investigate mathematical properties of pricing problems, in order to find structural properties, formulations and solution methods that are as efficient as possible. In particular, we focus our attention on pricing problems over a network. In this framework, an authority owns a subset of arcs and imposes tolls on them, in an attempt to maximise his/her revenue, while users travel on the network, seeking for their minimum cost path.

First, we provide a detailed review of the state of the art on bilevel pricing problems.

Then, we consider a particular case where the authority is using an unit toll scheme on his/her subset of arcs, imposing either the same toll on all of them, or a toll proportional to a given parameter particular to each arc (for instance a per kilometre toll). We show that if tolls are all equal then the complexity of the problem is polynomial, whereas in case of proportional tolls it is pseudo-polynomial.

We then address a robust approach taking into account uncertainty on parameters. We solve some polynomial cases of the pricing problem where uncertainty is considered using an interval representation.

Finally, we focus on another particular case where toll arcs are connected such that they constitute a path, as occurs on highways. We develop a Dantzig-Wolfe reformulation and present a Branch-and-Cut-and-Price algorithm to solve it. Several improvements are proposed, both for the column generation algorithm used to solve the linear relaxation and for the branching part used to find integer solutions. Numerical results are also presented to highlight the efficiency of the proposed strategies. This problem is proved to be APX-hard and a theoretical comparison between our model and another one from the literature is carried out.
Doctorat en Sciences
info:eu-repo/semantics/nonPublished

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35

Pfeiff, Daniel M. "Optimizing employment of search platforms to counter self-propelled semi-submersibles." Thesis, Monterey, Calif. : Naval Postgraduate School, 2009. http://edocs.nps.edu/npspubs/scholarly/theses/2009/Jun/09Jun%5FPfeiff.pdf.

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Thesis (M.S. in Operations Research)--Naval Postgraduate School, June 2009.
Thesis Advisor(s): Brown, Gerald G. "June 2009." Description based on title screen as viewed on July 14, 2009. Author(s) subject terms: Optimization, Mathematical Programming, Semi-Submersibles, Search and Detection, Defender-Attacker Optimization. Includes bibliographical references (p. 71-72). Also available in print.
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36

Kim, Chiheon. "Statistical limits of graphical channel models and a semidefinite programming approach." Thesis, Massachusetts Institute of Technology, 2018. http://hdl.handle.net/1721.1/120659.

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Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2018.
Cataloged from PDF version of thesis.
Includes bibliographical references (pages 205-213).
Community recovery is a major challenge in data science and computer science. The goal in community recovery is to find the hidden clusters from given relational data, which is often represented as a labeled hyper graph where nodes correspond to items needing to be labeled and edges correspond to observed relations between the items. We investigate the problem of exact recovery in the class of statistical models which can be expressed in terms of graphical channels. In a graphical channel model, we observe noisy measurements of the relations between k nodes while the true labeling is unknown to us, and the goal is to recover the labels correctly. This generalizes both the stochastic block models and spiked tensor models for principal component analysis, which has gained much interest over the last decade. We focus on two aspects of exact recovery: statistical limits and efficient algorithms achieving the statistic limit. For the statistical limits, we show that the achievability of exact recovery is essentially determined by whether we can recover the label of one node given other nodes labels with fairly high probability. This phenomenon was observed by Abbe et al. for generic stochastic block models, and called "local-to-global amplification". We confirm that local-to-global amplification indeed holds for generic graphical channel models, under some regularity assumptions. As a corollary, the threshold for exact recovery is explicitly determined. For algorithmic concerns, we consider two examples of graphical channel models, (i) the spiked tensor model with additive Gaussian noise, and (ii) the generalization of the stochastic block model for k-uniform hypergraphs. We propose a strategy which we call "truncate-and-relax", based on a standard semidefinite relaxation technique. We show that in these two models, the algorithm based on this strategy achieves exact recovery up to a threshold which orderwise matches the statistical threshold. We complement this by showing the limitation of the algorithm.
by Chiheon Kim.
Ph. D.
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37

Srinivasan, Subhashini. "Modeling the Homeschool timetabling problem using Integer programming." VCU Scholars Compass, 2011. http://scholarscompass.vcu.edu/etd/2555.

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Home schooling has steadily been increasing in the past decade. According to a survey in 2007, about 2.5 million children were being home schooled in the US. Typically, parents provide education at the convenience of their home and in some cases an instructor is appointed for the same. The Home School Timetabling problem (HSTP) deals with assigning subjects, timeslots and rooms to every student. In doing so, there are certain hard and specialty constraints that are to be satisfied. Integer programming (IP) has been used in solving the HSTP as it has the advantage of being able to provide information about the relative significance of each constraint with respect to the objective. A prototype in the form of a GUI has been built such that the parent can enter each student’s name, his/her subjects, duration, days and time for each subject, availability times of the parent etc. This data is then fed into the IP model so that it can generate a feasible timetable satisfying all of the constraints. When a solution is found it is formatted to provide the weekly timetable for each student, individually, as well as a complete timetable for all students each day.
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38

Petcharawises, Thavisakdi. "Programming language as a tool for software design." DigitalCommons@Robert W. Woodruff Library, Atlanta University Center, 1985. http://digitalcommons.auctr.edu/dissertations/2471.

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39

Zaibidi, Nerda Zura. "Modelling human fairness in cooperative games : a goal programming approach." Thesis, University of Portsmouth, 2012. https://researchportal.port.ac.uk/portal/en/theses/modelling-human-fairness-in-cooperative-games(4c3d0987-0edc-45be-9c4b-b1114df6bb3e).html.

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The issues of rationality in human behavior and fairness in cooperation have gained interest in various economic studies. In many prescriptive models of games, rationality of human decision makers implicitly assumes exchange-ability. This means that real people are assumed to adopt the beliefs of a player as expressed in the game when placed in the shoes of that particular player. However, it is a well debated topic in the literature that this modeling assumption is not in accordance to what behavioral economists have observed in some games played with real human subjects. Even when assuming the role of the same player in the game, different people think differently about the fairness of a particular outcome. People also view fairness as an essential ingredient of their decision making processes in games on cooperation. The aim of this research is to develop a new modeling approach to decision making in games on cooperation in which fairness is an important consideration. The satisficing and egilitarian philosophies on which weighted and Chebyshev Goal Programming (GP) rely, seem to offer an adequate and natural way for modeling human decision processes in at least the single-shot games of coordination that are investigated in this work. The solutions returned by the proposed GP approach aim to strike the right balance on several dimensions of con icting goals that are set by players themselves and that arise in the mental models these players have of other relevant players.
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40

Colombo, Marco. "Advances in interior point methods for large-scale linear programming." Thesis, University of Edinburgh, 2007. http://hdl.handle.net/1842/2488.

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This research studies two computational techniques that improve the practical performance of existing implementations of interior point methods for linear programming. Both are based on the concept of symmetric neighbourhood as the driving tool for the analysis of the good performance of some practical algorithms. The symmetric neighbourhood adds explicit upper bounds on the complementarity pairs, besides the lower bound already present in the common N−1 neighbourhood. This allows the algorithm to keep under control the spread among complementarity pairs and reduce it with the barrier parameter μ. We show that a long-step feasible algorithm based on this neighbourhood is globally convergent and converges in O(nL) iterations. The use of the symmetric neighbourhood and the recent theoretical under- standing of the behaviour of Mehrotra’s corrector direction motivate the introduction of a weighting mechanism that can be applied to any corrector direction, whether originating from Mehrotra’s predictor–corrector algorithm or as part of the multiple centrality correctors technique. Such modification in the way a correction is applied aims to ensure that any computed search direction can positively contribute to a successful iteration by increasing the overall stepsize, thus avoid- ing the case that a corrector is rejected. The usefulness of the weighting strategy is documented through complete numerical experiments on various sets of publicly available test problems. The implementation within the hopdm interior point code shows remarkable time savings for large-scale linear programming problems. The second technique develops an efficient way of constructing a starting point for structured large-scale stochastic linear programs. We generate a computation- ally viable warm-start point by solving to low accuracy a stochastic problem of much smaller dimension. The reduced problem is the deterministic equivalent program corresponding to an event tree composed of a restricted number of scenarios. The solution to the reduced problem is then expanded to the size of the problem instance, and used to initialise the interior point algorithm. We present theoretical conditions that the warm-start iterate has to satisfy in order to be successful. We implemented this technique in both the hopdm and the oops frameworks, and its performance is verified through a series of tests on problem instances coming from various stochastic programming sources.
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41

Sadones, Sylvie. "A new two-phase heuristic for two-dimensional rectangular bin-packing and strip-packing /." Thesis, McGill University, 1985. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=66036.

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42

Smith, Michael Anthony. "Embedding an object calculus in the unifying theories of programming." Thesis, University of Oxford, 2010. http://ora.ox.ac.uk/objects/uuid:8b5be90d-59c1-42c0-a996-ecd8015097b3.

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Hoare and He's Unifying Theories of Programming (UTP) provides a rich model of programs as relational predicates. This theory is intended to provide a single framework in which any programming paradigms, languages, and features, can be modelled, compared and contrasted. The UTP already has models for several programming formalisms, such as imperative programming, higher-order programming (e.g. programing with procedures), several styles of concurrent programming (or reactive systems), class-based object-orientation, and transaction processing. We believe that the UTP ought to be able to represent all significant computer programming language formalisms, in order for it to be considered a unifying theory. One gap in the UTP work is that of object-based object-orientation, such as that presented in Abadi and Cardelli's untyped object calculi (sigma-calculi). These sigma-calculi provide a prominent formalism of object-based object-oriented (OO) programs, which models programs as objects. We address this gap within this dissertation by presenting an embedding of an Abadi--Cardelli-style object calculus in the UTP. More formally, the thesis that his dissertation argues is that it is possible to provide an object-based object rientation to the UTP, with value- and reference-based objects, and a fully abstract model of references. We have made three contributions to our area of study: first, to extend the UTP with a notion of object-based object orientation, in contrast with the existing class-based models; second, to provide an alternative model of pointers (references) for the UTP that supports both value-based compound values (e.g. objects) and references (pointers), in contrast to existing UTP models with pointers that have reference-based compound values; and third, to model an Abadi-Cardelli notion of an object in the UTP, and thus demonstrate that it can unify this style of object formalism.
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43

Dong, Hongbo. "Copositive programming: separation and relaxations." Diss., University of Iowa, 2011. https://ir.uiowa.edu/etd/2692.

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A large portion of research in science and engineering, as well as in business, concerns one similar problem: how to make things "better”? Once properly modeled (although usually a highly nontrivial task), this kind of questions can be approached via a mathematical optimization problem. Optimal solution to a mathematical optimization problem, when interpreted properly, might corresponds to new knowledge, effective methodology or good decisions in corresponding application area. As already proved in many success stories, research in mathematical optimization has a significant impact on numerous aspects of human life. Recently, it was discovered that a large amount of difficult optimization problems can be formulated as copositive programming problems. Famous examples include a large class of quadratic optimization problems as well as many classical combinatorial optimization problems. For some more general optimization problems, copositive programming provides a way to construct tight convex relaxations. Because of this generality, new knowledge of copositive programs has the potential of being uniformly applied to these cases. While it is provably difficult to design efficient algorithms for general copositive programs, we study copositive programming from two standard aspects, its relaxations and its separation problem. With regard to constructing computational tractable convex relaxations for copositive programs, we develop direct constructions of two tensor relaxation hierarchies for the completely positive cone, which is a fundamental geometric object in copositive programming. We show connection of our relaxation hierarchies with known hierarchies. Then we consider the application of these tensor relaxations to the maximum stable set problem. With regard to the separation problem for copositive programming. We first prove some new results in low dimension of 5 x 5 matrices. Then we show how a separation procedure for this low dimensional case can be extended to any symmetric matrices with a certain block structure. Last but not least, we provide another approach to the separation and relaxations for the (generalized) completely positive cone. We prove some generic results, and discuss applications to the completely positive case and another case related to box-constrained quadratic programming. Finally, we conclude the thesis with remarks on some interesting open questions in the field of copositive programming.
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44

Richard, Jean-Philippe P. "Lifted inequalities for 0-1 mixed integer programming." Diss., Georgia Institute of Technology, 2002. http://hdl.handle.net/1853/24590.

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45

Bu, Honggang. "Scheduling Smart Home Appliances using Goal Programming with Priority." Thesis, North Dakota State University, 2016. https://hdl.handle.net/10365/28266.

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Driven by the advancement of smart electrical grid technologies, automated home energy management systems are being increasingly and extensively studied, developed, and widely accepted. A system like this is indispensable for and symbolic of a smart home. Mixed integer linear programming (MILP) together with dynamic electricity tariff and smart home appliances is a common way to developing energy management systems capable of automatically scheduling appliance operation and greatly saving monetary cost. This study transformed an existing plain MILP model to a goal programming model with priority to better address the conflict among each single appliance cost saving objective and user time preference objective. Constraints regarding the delays between pairs of closely related appliances are either extended or newly introduced. Numerical experiments on five appliances under different situations justify the validness of the proposed framework. Besides, the influences of key parameters on model performance are also investigated.
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46

Ginn, Isabella Brooke. "Integer Programming With Groebner Basis." VCU Scholars Compass, 2007. http://scholarscompass.vcu.edu/etd/769.

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Integer Programming problems are difficult to solve. The goal is to find an optimal solution that minimizes cost. With the help of Groebner based algorithms the optimal solution can be found if it exists. The application of the Groebner based algorithm and how it works is the topic of research. The Algorithms are The Conti-Traverso Algorithm and the Original Conti-Traverso Algorithm. Examples are given as well as proofs that correspond to the algorithms. The latter algorithm is more efficient as well as user friendly. The algorithms are not necessarily the best way to solve and integer programming problem, but they do find the optimal solution if it exists.
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Valiron, Benoit. "A functional programming language for quantum computation with classical control." Thesis, University of Ottawa (Canada), 2004. http://hdl.handle.net/10393/26790.

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The objective of this thesis is to develop a functional programming language for quantum computers based on the QRAM model, following the work of P. Selinger (2004) on quantum flow-charts. We construct a lambda-calculus without side-effects to deal with quantum bits. We equip this calculus with a probabilistic call-by-value operational semantics. Since quantum information cannot be duplicated due to the no-cloning property, we need a resource-sensitive type system. We develop it based on affine intuitionistic linear logic. Unlike the quantum lambda-calculus proposed by Van Tonder (2003, 2004), the resulting lambda-calculus has only one lambda-abstraction, linear and non-linear abstractions being encoded in the type system. We also integrate classical and quantum data types within our language. The main results of this work are the subject-reduction of the language and the construction of a type inference algorithm.
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48

Bengtsson, Maja. "Att undervisa i programmering utan programmeringsutbildning.En intervjustudie hur lärare utan utbildning i programmering implementerar programmering i sin undervisning." Thesis, Örebro universitet, Institutionen för naturvetenskap och teknik, 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:oru:diva-92897.

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In the fall of 2018, programming was implemented in the swedish curriculum and then became a new element in mathematics education for grades 1-3. Teachers who took their degree before the implementation, lacks education in programming and there is interest in finding out how teaching about programming is conducted since it became part of the curriculum. The purpose of this study was to contribute with knowledge about how teachers have implemented programming in their teaching even though they lack education in it. Four semi-structured interviews have been conducted where the data from the interviews has been analyzed from Mathematical Knowledge for Teaching. The result shows that teachers without education in programming find it difficult to plan instruction in programming by themselves. In the teaching of programming the teachers focus on the central concepts in programming and that the programming should interest the students. It was difficult for teachers to assess the students in programming and the only assessment that teachers make is the formative assessment.
Sammanfattning Hösten 2018 implementerades programmering i den svenska läroplanen och blev då ett nytt moment inom matematikundervisningen för årskurs 1-3. Lärare som innan detta tog sin lärarexamen saknar utbildning inom programmering och det finns intresse att ta reda på hur undervisningen kring programmering bedrivs sedan det blev en del av läroplanen. Syftet med denna studie var att bidra med kunskap om hur lärare har implementerat programmering i sin undervisning trots att de saknar utbildning inom det. Fyra stycken semistrukturerade intervjuer har gjorts där datan från intervjuerna har analyserats utifrån Mathematical Knowledge for Teaching. Resultatet visar på att lärare utan utbildning inom programmering har svårigheter att på egen hand planera undervisning i programmering. Under genomförandet av undervisningen fokuserar lärarna på att befästa centrala begrepp inom programmering och att väcka ett intresse hos eleverna. Det upplevdes svårt för lärarna att bedöma eleverna inom programmering och den enda bedömning som lärarna gör är den formativa bedömningen.
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49

de, Castro Christopher H. "Assessing the Impact of Computer Programming in Understanding Limits and Derivatives in a Secondary Mathematics Classroom." Digital Archive @ GSU, 2011. http://digitalarchive.gsu.edu/msit_diss/79.

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This study explored the development of student’s conceptual understanding of limit and derivative when specific computational tools were utilized. Fourteen students from a secondary Advanced Placement Calculus AB course explored the limit and derivative concepts from calculus using computational tools in the Maple computer algebra system. Students worked in pairs utilizing the pair-programming collaborative model. Four groups of student pairs constructed computational tools and used them to explore the limit and derivative concepts. The remaining four student pairs were provided similar tools and asked to perform identical explorations. A multiple embedded case design was utilized to explore ways students in two classes, a programming class P and a non-programming class N, constructed understandings focusing upon their interactions with each other and with the computational tools. The Action-Process-Object-Schema (APOS) conceptual model and Constructionist framework guided design and construction of the tools, outlined developmental goals and milestones, and provided interpretive context for analysis. Results provided insights into the effective design and use of computational tools in fostering conceptual understanding. The study found the additional burden of programming redirected students’ attention away from the intended conceptual understandings. The study additionally found, however, that pre-constructed tools effectively promote conceptual understanding of the limit concept when coupled with a mature conceptual model of development. Four themes influencing development of these understandings emerged: An instructional focus on skills over concepts, the instructional sequence, the willingness and ability of students to adopt and utilize computational tools, and the ways cognitive conflict was mediated.
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50

Fukasawa, Ricardo. "Single-row mixed-integer programs : theory and computations /." Diss., Atlanta, Ga. : Georgia Institute of Technology, 2008. http://hdl.handle.net/1853/24660.

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Thesis (Ph.D.)--Industrial and Systems Engineering, Georgia Institute of Technology, 2009.
Committee Chair: William J. Cook; Committee Member: Ellis Johnson; Committee Member: George Nemhauser; Committee Member: Robin Thomas; Committee Member: Zonghao Gu
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