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Journal articles on the topic 'Parametric programs'

Author: Grafiati

Published: 6 September 2023

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1

Janakiraman, Ganesh, and Sridhar Seshadri. "Parametric concavity in stochastic dynamic programs." Computers & Industrial Engineering 61, no. 1 (August 2011): 98–102. http://dx.doi.org/10.1016/j.cie.2011.02.017.

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2

El-Kafrawy, M. M., N. A. El-Ramly, and R. A. Mahmoud. "On fuzzy convexity of parametric programs." Microelectronics Reliability 26, no. 2 (January 1986): 235–39. http://dx.doi.org/10.1016/0026-2714(86)90717-1.

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3

Warburton, A. R. "Parametric Solution of Bicriterion Linear Fractional Programs." Operations Research 33, no. 1 (February 1985): 74–84. http://dx.doi.org/10.1287/opre.33.1.74.

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4

Glover, Fred. "Parametric tabu-search for mixed integer programs." Computers & Operations Research 33, no. 9 (September 2006): 2449–94. http://dx.doi.org/10.1016/j.cor.2005.07.009.

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5

Nieszporek, Tadeusz, and Andrzej Piotrowski. "Parametric Programming of CNC Machine Tools." Applied Mechanics and Materials 282 (January 2013): 203–10. http://dx.doi.org/10.4028/www.scientific.net/amm.282.203.

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CNC machine tools are increasingly often used in industry, and the development of the methods of their programming is also proceeding. Modern multipurpose multi-axial machine tools are programmed using special CAD/CAM software programs. Universal special programs for controlling CNC machine tools can, however, be generated in programs written in high-level languages. An example can be the machining of gears on universal CNC machine tools using versatile machining tools.

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6

Fiacco, Anthony V. "Global multi-parametric optimal value bounds and solution estimates for separable parametric programs." Annals of Operations Research 27, no. 1 (December 1990): 381–95. http://dx.doi.org/10.1007/bf02055203.

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7

DRABENT, WŁODZIMIERZ, JAN MAŁUSZYŃSKI, and PAWEŁ PIETRZAK. "Using parametric set constraints for locating errors in CLP programs." Theory and Practice of Logic Programming 2, no. 4-5 (July 2002): 549–610. http://dx.doi.org/10.1017/s1471068402001473.

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This paper introduces a framework of parametric descriptive directional types for Constraint Logic Programming (CLP). It proposes a method for locating type errors in CLP programs, and presents a prototype debugging tool. The main technique used is checking correctness of programs w.r.t. type specifications. The approach is based on a generalization of known methods for proving the correctness of logic programs to the case of parametric specifications. Set constraint techniques are used for formulating and checking verification conditions for (parametric) polymorphic type specifications. The specifications are expressed in a parametric extension of the formalism of term grammars. The soundness of the method is proved, and the prototype debugging tool supporting the proposed approach is illustrated on examples. The paper is a substantial extension of the previous work by the same authors concerning monomorphic directional types.

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8

Fu, Norie, and Takafumi Shibuta. "An algebraic algorithm for solving parametric integer programs." Discrete Applied Mathematics 245 (August 2018): 253–64. http://dx.doi.org/10.1016/j.dam.2017.09.001.

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9

Jiao, Hongwei, Yong-Qiang Chen, and Wei-Xin Cheng. "A Novel Optimization Method for Nonconvex Quadratically Constrained Quadratic Programs." Abstract and Applied Analysis 2014 (2014): 1–11. http://dx.doi.org/10.1155/2014/698489.

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This paper presents a novel optimization method for effectively solving nonconvex quadratically constrained quadratic programs (NQCQP) problem. By applying a novel parametric linearizing approach, the initial NQCQP problem and its subproblems can be transformed into a sequence of parametric linear programs relaxation problems. To enhance the computational efficiency of the presented algorithm, a cutting down approach is combined in the branch and bound algorithm. By computing a series of parametric linear programs problems, the presented algorithm converges to the global optimum point of the NQCQP problem. At last, numerical experiments demonstrate the performance and computational superiority of the presented algorithm.

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Jiao, Hongwei, and Rongjiang Chen. "A parametric linearizing approach for quadratically inequality constrained quadratic programs." Open Mathematics 16, no. 1 (April 20, 2018): 407–19. http://dx.doi.org/10.1515/math-2018-0037.

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AbstractIn this paper we propose a new parametric linearizing approach for globally solving quadratically inequality constrained quadratic programs. By utilizing this approach, we can derive the parametric linear programs relaxation problem of the investigated problem. To accelerate the computational speed of the proposed algorithm, an interval deleting rule is used to reduce the investigated box. The proposed algorithm is convergent to the global optima of the initial problem by subsequently partitioning the initial box and solving a sequence of parametric linear programs relaxation problems. Finally, compared with some existing algorithms, numerical results show higher computational efficiency of the proposed algorithm.

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11

Pertsinidis, A., I. E. Grossmann, and G. J. McRae. "Parametric optimization of MILP programs and a framework for the parametric optimization of MINLPs." Computers & Chemical Engineering 22 (March 1998): S205—S212. http://dx.doi.org/10.1016/s0098-1354(98)00056-8.

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12

Park, Jihyeok, Hongki Lee, and Sukyoung Ryu. "A Survey of Parametric Static Analysis." ACM Computing Surveys 54, no. 7 (July 2021): 1–37. http://dx.doi.org/10.1145/3464457.

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Understanding program behaviors is important to verify program properties or to optimize programs. Static analysis is a widely used technique to approximate program behaviors via abstract interpretation. To evaluate the quality of static analysis, researchers have used three metrics: performance, precision, and soundness. The static analysis quality depends on the analysis techniques used, but the best combination of such techniques may be different for different programs. To find the best combination of analysis techniques for specific programs, recent work has proposed parametric static analysis . It considers static analysis as black-box parameterized by analysis parameters , which are techniques that may be configured without analysis details. We formally define the parametric static analysis, and we survey analysis parameters and their parameter selection in the literature. We also discuss open challenges and future directions of the parametric static analysis.

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13

Roll, Jacob. "Piecewise Linear Solution Paths for Parametric Piecewise Quadratic Programs." IFAC Proceedings Volumes 41, no. 2 (2008): 2732–37. http://dx.doi.org/10.3182/20080706-5-kr-1001.00460.

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14

Kotlobovskii, I. B., M. M. Budanova, and E. N. Lukash. "DEVELOPMENT POTENTIAL OF REGIONAL PARAMETRIC INSURANCE PROGRAMS IN RUSSIA." Finance: Theory and Practice 22, no. 2 (May 26, 2018): 106–23. http://dx.doi.org/10.26794/2587-5671-2018-22-2-106-123.

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15

Klatte, D. "Lower Semicontinuity of the Minimum in Parametric Convex Programs." Journal of Optimization Theory and Applications 94, no. 2 (August 1997): 511–17. http://dx.doi.org/10.1023/a:1022652216355.

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16

Köppe, M., M. Queyranne, and C. T. Ryan. "Parametric Integer Programming Algorithm for Bilevel Mixed Integer Programs." Journal of Optimization Theory and Applications 146, no. 1 (February 18, 2010): 137–50. http://dx.doi.org/10.1007/s10957-010-9668-3.

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17

Tang, Shuai, Yuzhen Chen, and Yunrui Guo. "An effective algorithm for globally solving quadratic programs using parametric linearization technique." Open Mathematics 16, no. 1 (November 10, 2018): 1300–1312. http://dx.doi.org/10.1515/math-2018-0108.

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AbstractIn this paper, we present an effective algorithm for globally solving quadratic programs with quadratic constraints, which has wide application in engineering design, engineering optimization, route optimization, etc. By utilizing new parametric linearization technique, we can derive the parametric linear programming relaxation problem of the quadratic programs with quadratic constraints. To improve the computational speed of the proposed algorithm, some interval reduction operations are used to compress the investigated interval. By subsequently partitioning the initial box and solving a sequence of parametric linear programming relaxation problems the proposed algorithm is convergent to the global optimal solution of the initial problem. Finally, compared with some known algorithms, numerical experimental results demonstrate that the proposed algorithm has higher computational efficiency.

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18

Perkasa, Lugantha. "Automated generation of CNC programs for manufacturing: A Review." Journal of Mechanical Science and Engineering 6, no. 2 (July 8, 2020): 035–39. http://dx.doi.org/10.36706/jmse.v6i2.33.

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A configuration system for a product and model requires a parametric design. Where the system is made first, the first thing that needs to be done is the determination of the model. In this journal will discuss the configuration model that is the application of parametric design methods in the MTO environment. CNC program, the result is a variant of a product with good quality so that it can increase the production quantity. High potential short production time costs incurred a little and increase profits. CNC programs are made with various parameters then proceed with a product configuration system that will automatically run in the CNC program.

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19

Simatupang, Adolf T. "Program Linier Parametrik." Desimal: Jurnal Matematika 2, no. 1 (January 30, 2019): 69–76. http://dx.doi.org/10.24042/djm.v2i1.4184.

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This study aims to discuss a linear program problem where its constants can change, If a constant for a linear program problem is changed, then we don't need to count from the beginning again. Next, we will examine the properties of the objective function as a result of changes in these constants. In this discussion determine the non-negative "critical value" which provides the optimal solution to the problem of parametric linear programs. Searching for critical values in parametric linear programs is done by the matrix version method.

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20

Katz, Gal, and Doron Peled. "Synthesis of Parametric Programs using Genetic Programming and Model Checking." Electronic Proceedings in Theoretical Computer Science 140 (February 23, 2014): 70–84. http://dx.doi.org/10.4204/eptcs.140.5.

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21

Smith, D. A. "Parametric cubic spline-fitting programs for open and closed curves." Computers in Physics 6, no. 5 (1992): 472. http://dx.doi.org/10.1063/1.168433.

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22

Bouza, Gemayqze, Jürgen Guddat, and Georg Still. "Critical sets in one-parametric mathematical programs with complementarity constraints." Optimization 57, no. 2 (April 2008): 319–36. http://dx.doi.org/10.1080/02331930701779955.

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23

Poore, Aubrey B. "Bifurcation Problems for Some Parametric Nonlinear Programs in Banach Spaces." SIAM Journal on Control and Optimization 34, no. 6 (November 1996): 1947–71. http://dx.doi.org/10.1137/s0363012994277165.

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24

El-Kafrawy, M. M., N. A. El-Ramly, and R. A. Mahmoud. "Fuzzy convex cones and functions for ordinary and parametric programs." Microelectronics Reliability 26, no. 2 (January 1986): 241–45. http://dx.doi.org/10.1016/0026-2714(86)90718-3.

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25

Best, M. J., and B. Ding. "On the continuity of the minimum in parametric quadratic programs." Journal of Optimization Theory and Applications 86, no. 1 (July 1995): 245–50. http://dx.doi.org/10.1007/bf02193469.

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26

Dolgikh, T. A. "PARAMETRIC MODELING IN ARCHITECTURE ON THE EXAMPLE OF CREATIVITY OF ZAHA HADID." Regional problems of architecture and urban planning, no. 14 (December 29, 2020): 86–95. http://dx.doi.org/10.31650/2707-403x-2020-14-86-95.

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Modern architecture is parametric architecture. Parametric entered our life not only through architecture, but also through design, fashion, industry, art. Zaha Hadid’s leading architects for many years successfully working in the style of parametric. Although parametric is rooted in digital animation techniques of the mid-1990s, it only became fully apparent in recent years with the development of advanced parametric computer programs. The so-called digital architecture, closely associated with programming, automatically converts volume, making it technically and economically feasible. Using computer programs, we can create a “thinking” building. Using the morphogenesis algorithm applied to different situations, we get unique buildings that are members of the same “population”. The most modern example of analysis allows us to determine the patterns of regional development by 25 parameters. Programmers have developed various scripts that form blocks around the perimeter, depending on the size of the land, proportion and orientation. These scripts are used in their work by leading architects in the field of parametric. This is best seen in the master plans of Zaha Hadid. Thus, the dynamic parametric architecture doesn’t create a separate building, but integrates it into the structure of space, linking modern architecture with the historical development of the city.

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27

SISARAT, NITHIRAT, RATTANAPORN WANGKEEREE, and RABIAN WANGKEEREE. "Strong duality in parametric robust semi-definite linear programming and exact relaxations." Carpathian Journal of Mathematics 39, no. 2 (December 21, 2022): 477–90. http://dx.doi.org/10.37193/cjm.2023.02.10.

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This paper addresses the issue of which strong duality holds between parametric robust semi-definite linear optimization problems and their dual programs. In the case of a spectral norm uncertainty set, it yields a corresponding strong duality result with a semi-definite programming as its dual. We also show that the dual can be reformulated as a second-order cone programming problem or a linear programming problem when the constraint uncertainty sets of parametric robust semi-definite linear programs are given in terms of affinely parameterized diagonal matrix.

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28

FAGES, FRANÇOIS, and EMMANUEL COQUERY. "Typing constraint logic programs." Theory and Practice of Logic Programming 1, no. 6 (November 2001): 751–77. http://dx.doi.org/10.1017/s1471068401001120.

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We present a prescriptive type system with parametric polymorphism and subtyping for constraint logic programs. The aim of this type system is to detect programming errors statically. It introduces a type discipline for constraint logic programs and modules, while maintaining the capabilities of performing the usual coercions between constraint domains, and of typing meta-programming predicates, thanks to the exibility of subtyping. The property of subject reduction expresses the consistency of a prescriptive type system w.r.t. the execution model: if a program is ‘well-typed’, then all derivations starting from a ‘well-typed’ goal are again ‘well-typed’. That property is proved w.r.t. the abstract execution model of constraint programming which proceeds by accumulation of constraints only, and w.r.t. an enriched execution model with type constraints for substitutions. We describe our implementation of the system for type checking and type inference. We report our experimental results on type checking ISO-Prolog, the (constraint) libraries of Sicstus Prolog and other Prolog programs.

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29

Feicht, Louis. "Parametric Equations, Maple, and Tubeplots." Mathematics Teacher 90, no. 8 (November 1997): 612–13. http://dx.doi.org/10.5951/mt.90.8.0612.

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Parametric equations pose a problem for many students. Often students are unable to generate graphical representations quickly and find it difficult to interpret the “invisible” parameter. Such symbolic programs as Maple have parametric graphing capabilities built into them. Maple also has a form of graphing output called tubeplots, which requires the use of parametric functions. I have taught parametric graphing using tubeplots over the past four years. The mystery of parametric equations disappears with this hands-on approach as students create symbolic representations of functions from the graphical representations. This approach differs from the typical presentation of parametric equations in which students must create a graph from a symbolic representation. This activity establishes a graphical foundation for parametric equations and provides a comprehensive review and exploration of many previously learned topics.

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30

Östermark, Ralf. "SENSITIVITY ANALYSIS OF FUZZY LINEAR PROGRAMS: AN APPROACH TO PARAMETRIC INTERDEPENDENCE." Kybernetes 16, no. 2 (February 1987): 113–20. http://dx.doi.org/10.1108/eb005762.

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31

Zhang, Xiang-Sun, and De-Gang Liu. "A note on the continuity of solutions of parametric linear programs." Mathematical Programming 47, no. 1-3 (May 1990): 143–53. http://dx.doi.org/10.1007/bf01580857.

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32

Doroshenko, A. Yu, and I. Z. Achour. "Automated generation of programs for a class of parametric neuroevolution algorithms." PROBLEMS IN PROGRAMMING, no. 3-4 (December 2022): 301–10. http://dx.doi.org/10.15407/pp2022.03-04.301.

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The facilities of algebra of hyperschemes are applied for automated generation of neuroevolution algorithms on an example of a binary multiplexer evaluation problem, which is a part of the SharpNEAT system. SharpNEAT is an open-source framework developed in C# programming language, which implements a genetic neuroevolution algorithm for the .NET platform. Neuroevolution is a form of artificial intelligence, which uses evolution algorithms for creating neural networks, parameters, topology, and rules. Evolution algorithms apply mutation, recombination, and selection mechanisms for finding neural networks with behavior that satisfies to conditions of some formally defined problem. In this paper, we demonstrate the use of algebra of algorithms and hyperschemes for the automated generation of evaluation programs for neuroevolution problems. Hyperscheme is a high-level parameterized specification of an algorithm for solving some class of problems. Setting the values of the hyperscheme parameters and further interpretation of a hyperscheme allows obtaining algorithms adapted to specific conditions of their use. Automated construction of hyperschemes and generation of algorithms based on them is implemented in the developed integrated toolkit for design and synthesis of programs. The design of algorithms is based on Glushkov systems of algorithmic algebra. The schemes are built using a dialogue constructor of syntactically correct programs, which consists in descending design of algorithms by detailing the constructions of algorithmic language. The design is represented as an algorithm tree. Based on algorithm schemes, programs in a target programming language are generated. The results of the experiment consisting in executing the generated binary multiplexer evaluating program on a cloud platform are given.

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33

LIU, YONGCHAO. "STABILITY ANALYSIS OF PARAMETRIC GENERALIZED EQUATIONS AND APPLICATIONS." Asia-Pacific Journal of Operational Research 30, no. 05 (October 2013): 1350017. http://dx.doi.org/10.1142/s0217595913500176.

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The paper studies the stability of parametric generalized equations (PGE) defined by adding two set-valued mappings. Under some moderate conditions, the open covering/metric regularity of the solution mapping of PGE are discussed. The results are used to analyze the stability of stochastic generalized equations and parametric mathematical programs with equilibrium constraints.

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NEIS, GEORG, DEREK DREYER, and ANDREAS ROSSBERG. "Non-parametric parametricity." Journal of Functional Programming 21, no. 4-5 (September 2011): 497–562. http://dx.doi.org/10.1017/s0956796811000165.

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AbstractType abstraction and intensional type analysis are features seemingly at odds—type abstraction is intended to guarantee parametricity and representation independence, while type analysis is inherently non-parametric. Recently, however, several researchers have proposed and implemented “dynamic type generation” as a way to reconcile these features. The idea is that, when one defines an abstract type, one should also be able to generate at runtime a fresh type name, which may be used as a dynamic representative of the abstract type for purposes of type analysis. The question remains: in a language with non-parametric polymorphism, does dynamic type generation provide us with the same kinds of abstraction guarantees that we get from parametric polymorphism?Our goal is to provide a rigorous answer to this question. We define a step-indexed Kripke logical relation for a language with both non-parametric polymorphism (in the form of type-safe cast) and dynamic type generation. Our logical relation enables us to establish parametricity and representation independence results, even in a non-parametric setting, by attaching arbitrary relational interpretations to dynamically generated type names. In addition, we explore how programs that are provably equivalent in a more traditional parametric logical relation may be “wrapped” systematically to produce terms that are related by our non-parametric relation, and vice versa. This leads us to develop a “polarized” variant of our logical relation, which enables us to distinguish formally between positive and negative notions of parametricity.

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35

Suchocka, Marzena, Kinga Kimic, and Aleksandra Widaj. "Narzędzia stosowane w projektowaniu parametrycznym w architekturze krajobrazu." ACTA SCIENTIARUM POLONORUM - Architectura Budownictwo 18, no. 3 (November 28, 2019): 79–86. http://dx.doi.org/10.22630/aspa.2019.18.3.37.

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In the era of digitization, parametric design creates new possibilities for its application in areas such as architecture and design as well as landscape architecture. However, it requires tools that can not only facilitate the design process, but also reduce its time consumption. The purpose of the article is to review the software used for parametric design supporting the work of landscape architects. The selected, most popular programs and plugins used by architects and designers, which are also indirectly used by landscape architects as well as software dedicated directly to landscape architects, were evaluated. Most of the discussed software has options for parametric design, while they only apply to selected elements. Due to the interdisciplinary character of landscape architecture, there is currently no single multifunctional program giving the possibility of comprehensive application of parametric design options to all aspects of a complex project. For this reason, landscape architects are forced to combine functions themselves using several of programs. This is a significant difficulty in carrying out the design process.

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36

Chen, Zhangyou, and Zhe Chen. "Optimality Conditions for Nonsmooth Generalized Semi-Infinite Programs." Abstract and Applied Analysis 2013 (2013): 1–8. http://dx.doi.org/10.1155/2013/131938.

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We consider a class of nonsmooth generalized semi-infinite programming problems. We apply results from parametric optimization to the lower level problems of generalized semi-infinite programming problems to get estimates for the value functions of the lower level problems and thus derive necessary optimality conditions for generalized semi-infinite programming problems. We also derive some new estimates for the value functions of the lower level problems in terms of generalized differentiation and further obtain the necessary optimality conditions.

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37

Jones, R. Kenny, Paul Guerrero, Niloy J. Mitra, and Daniel Ritchie. "ShapeCoder: Discovering Abstractions for Visual Programs from Unstructured Primitives." ACM Transactions on Graphics 42, no. 4 (July 26, 2023): 1–17. http://dx.doi.org/10.1145/3592416.

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We introduce ShapeCoder, the first system capable of taking a dataset of shapes, represented with unstructured primitives, and jointly discovering (i) useful abstraction functions and (ii) programs that use these abstractions to explain the input shapes. The discovered abstractions capture common patterns (both structural and parametric) across a dataset, so that programs rewritten with these abstractions are more compact, and suppress spurious degrees of freedom. ShapeCoder improves upon previous abstraction discovery methods, finding better abstractions, for more complex inputs, under less stringent input assumptions. This is principally made possible by two methodological advancements: (a) a shape-to-program recognition network that learns to solve sub-problems and (b) the use of e-graphs, augmented with a conditional rewrite scheme, to determine when abstractions with complex parametric expressions can be applied, in a tractable manner. We evaluate ShapeCoder on multiple datasets of 3D shapes, where primitive decompositions are either parsed from manual annotations or produced by an unsupervised cuboid abstraction method. In all domains, ShapeCoder discovers a library of abstractions that captures high-level relationships, removes extraneous degrees of freedom, and achieves better dataset compression compared with alternative approaches. Finally, we investigate how programs rewritten to use discovered abstractions prove useful for downstream tasks.

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38

Lu, Mo Wu, Xu Yang, and Chang Lu. "Parametric Design of Wave Spring Based on SolidWorks." Advanced Materials Research 753-755 (August 2013): 1262–65. http://dx.doi.org/10.4028/www.scientific.net/amr.753-755.1262.

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This paper introduces a parametric modeling method of wave spring. The common wave spring parametric design programs are written with VBA in the SolidWorks platform by calling the relevant API (application program interface) functions according to the spring entity structure characteristics and service conditions, which obviously reduces the designers repetitive operations in the modeling process and shortens the spring design cycle.

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39

Kuno, Takahito, and Jianming Shi. "Linear programs with an additional separable concave constraint." Journal of Applied Mathematics and Decision Sciences 8, no. 3 (January 1, 2004): 155–74. http://dx.doi.org/10.1155/s1173912604000100.

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In this paper, we develop two algorithms for globally optimizing a special class of linear programs with an additional concave constraint. We assume that the concave constraint is defined by a separable concave function. Exploiting this special structure, we apply Falk-Soland's branch-and-bound algorithm for concave minimization in both direct and indirect manners. In the direct application, we solve the problem alternating local search and branch-and-bound. In the indirect application, we carry out the bounding operation using a parametric right-hand-side simplex algorithm.

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40

Mu, Rui, Na Zhao, and Yong Jun Pan. "A Secondary Development System on Grader Working Device Oriented to Mechanism Optimization." Applied Mechanics and Materials 84-85 (August 2011): 115–19. http://dx.doi.org/10.4028/www.scientific.net/amm.84-85.115.

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Because of the complex structure of grader working device, its optimization is a repeated, continuously improved process. A new model has to be set up before each optimization. In order to solve the problem of repeating modeling and improve the product optimization efficiency, a second development system of working device is established. Parametric driving about working device is realized in term of spatial mechanism. At first, the overall design framework of this second development system was established, then customized user interface was completed based on UG/Open API and parametric programs about the working device system were complied based on UG/Open Grip subsequently. The connection among customized user interface, parametric programs and human-computer interaction was realized by using Visual C++, the integrated second development system design of working device was eventually completed. This second development system could not only provide engineers with a rapid design method to shorten the new product development cycle, but solve the problem of repeating modeling during optimization design as well.

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41

Feng, Fang, Hui Pan, and Guo Jun Hu. "PRO/E Based Parametric Design of Spur Gears." Advanced Materials Research 201-203 (February 2011): 790–94. http://dx.doi.org/10.4028/www.scientific.net/amr.201-203.790.

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This paper adopts the method of PRO/E programs, relationships and parameters to conduct the parametric design process for various types of spur gears, analyzes the key parameters of the spur gears, defines them via programming, and by the use of parameters dialog box and relationships dialog box to define basic parameters and the relationships between them step by step, finally to complete the gear’s parametric model.

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42

Gong, Yu-Jun, and Yong Xia. "On Sufficient Global Optimality Conditions for Bivalent Quadratic Programs with Quadratic Constraints." Asia-Pacific Journal of Operational Research 32, no. 04 (July 23, 2015): 1550025. http://dx.doi.org/10.1142/s0217595915500256.

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We show the recent sufficient global optimality condition for the quadratic constrained bivalent quadratic optimization problem is equivalent to verify the zero duality gap. Then, based on the optimal parametric Lagrangian dual model, we establish improved sufficient conditions by strengthening the dual bound.

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43

Guo, Lei, Gui-Hua Lin, and Jane J. Ye. "Stability Analysis for Parametric Mathematical Programs with Geometric Constraints and Its Applications." SIAM Journal on Optimization 22, no. 3 (January 2012): 1151–76. http://dx.doi.org/10.1137/120868657.

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44

Gade, Dinakar, Simge Küçükyavuz, and Suvrajeet Sen. "Decomposition algorithms with parametric Gomory cuts for two-stage stochastic integer programs." Mathematical Programming 144, no. 1-2 (November 30, 2012): 39–64. http://dx.doi.org/10.1007/s10107-012-0615-y.

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45

Kailey, Navdeep, N. A. Sonali, and Vikas Sharma. "Parametric approach for a class of fractional variational programs involving support functions." International Journal of Mathematics in Operational Research 23, no. 4 (2022): 481. http://dx.doi.org/10.1504/ijmor.2022.127756.

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46

Sharma, Vikas, Sonali ., and Navdeep Kailey. "Parametric approach for a class of fractional variational programs involving support functions." International Journal of Mathematics in Operational Research 1, no. 1 (2021): 1. http://dx.doi.org/10.1504/ijmor.2021.10052128.

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Cambini, Riccardo, and Claudio Sodini. "A parametric solution algorithm for a class of rank-two nonconvex programs." Journal of Global Optimization 60, no. 4 (October 13, 2013): 649–62. http://dx.doi.org/10.1007/s10898-013-0115-5.

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Khalilpour, Rajab, and I. A. Karimi. "Parametric optimization with uncertainty on the left hand side of linear programs." Computers & Chemical Engineering 60 (January 2014): 31–40. http://dx.doi.org/10.1016/j.compchemeng.2013.08.005.

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Kassem, Mohamed Abd El-Hady. "Characterization of the stability set for non-differentiable fuzzy parametric optimization problems." International Journal of Mathematics and Mathematical Sciences 2005, no. 12 (2005): 1995–2003. http://dx.doi.org/10.1155/ijmms.2005.1995.

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Abstract:

This note presents the characterization of the stability set of the first kind for multiobjective nonlinear programming (MONLP) problems with fuzzy parameters either in the constraints or in the objective functions without any differentiability assumptions. These fuzzy parameters are characterized by triangular fuzzy numbers (TFNs). The existing results concerning the parametric space in convex programs are reformulated to study for multiobjective nonlinear programs under the concept ofα-Pareto optimality.

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Li, Xian Zhi, Xin Zhou, Li Juan Wang, and Chun Shan Liu. "Study on Parametric Drawing of Planetary Gear Transmission." Advanced Materials Research 308-310 (August 2011): 2215–19. http://dx.doi.org/10.4028/www.scientific.net/amr.308-310.2215.

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Abstract:

In the planetary gear transmission design, the structure and shape of some major parts are often the same or similar, tedious and duplicate drawing may reduce the drawing efficiency. This paper studies redevelopment technology by using Visual Lisp language in AutoCAD platform, and compiles drawing programs to realize parametric drawing. The new graph can be generated automatically by a computer by modifying simply a few parameters in the drawing process.

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