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Relevant bibliographies by topics / Linear programming

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Academic literature on the topic 'Linear programming'

Author: Grafiati

Published: 4 June 2021

Last updated: 9 June 2025

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Journal articles on the topic "Linear programming"

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Asquith, J., and Vasek Chvatal. "Linear Programming." Mathematical Gazette 69, no. 448 (June 1985): 151. http://dx.doi.org/10.2307/3616957.

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Caoimh, C. C. O., and Howard Karloff. "Linear Programming." Mathematical Gazette 79, no. 484 (March 1995): 245. http://dx.doi.org/10.2307/3620128.

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Dantzig, George B. "Linear Programming." Operations Research 50, no. 1 (February 2002): 42–47. http://dx.doi.org/10.1287/opre.50.1.42.17798.

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Římánek, Josef. "Linear programming." European Journal of Operational Research 21, no. 2 (August 1985): 277–78. http://dx.doi.org/10.1016/0377-2217(85)90046-3.

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Qi, Zhiquan, Yingjie Tian, and Yong Shi. "Regularized Multiple Criteria Linear Programming via Linear Programming." Procedia Computer Science 9 (2012): 1234–39. http://dx.doi.org/10.1016/j.procs.2012.04.134.

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S. Mohan, S. Mohan, and Dr S. Sekar Dr. S. Sekar. "Linear Programming Problem with Homogeneous Constraints." Indian Journal of Applied Research 4, no. 3 (October 1, 2011): 298–307. http://dx.doi.org/10.15373/2249555x/mar2014/90.

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D, Sempavazhaam, Jothi K, and Kamali S. Nandhini A. Princy Rebekah J. "A Study on Linear Programming Problem." International Journal of Trend in Scientific Research and Development Volume-3, Issue-2 (February 28, 2019): 903–4. http://dx.doi.org/10.31142/ijtsrd21539.

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Mahjoub Mohammed Hussein, Elfarazdag. "Application of Linear Programming (Transportation Problem)." International Journal of Science and Research (IJSR) 12, no. 3 (March 5, 2023): 452–54. http://dx.doi.org/10.21275/sr21222020051.

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Dangerfield, Janet, and B. D. Bunday. "Basic Linear Programming." Mathematical Gazette 69, no. 450 (December 1985): 317. http://dx.doi.org/10.2307/3617607.

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Megiddo, N. "Linear Programming (1986)." Annual Review of Computer Science 2, no. 1 (June 1987): 119–45. http://dx.doi.org/10.1146/annurev.cs.02.060187.001003.

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Dissertations / Theses on the topic "Linear programming"

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Andreotti, Sandro [Verfasser]. "Linear Programming and Integer Linear Programming in Bioinformatics / Sandro Andreotti." Berlin : Freie Universität Berlin, 2015. http://d-nb.info/1066645213/34.

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Sarrabezolles, Pauline. "Colourful linear programming." Thesis, Paris Est, 2015. http://www.theses.fr/2015PESC1033/document.

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Le théorème de Carathéodory coloré, prouvé en 1982 par Bárány, énonce le résultat suivant. Etant donnés d Å1 ensembles de points S1,SdÅ1 dans Rd , si chaque Si contient 0 dans son enveloppe convexe, alors il existe un sous-ensemble arc-en-ciel T µ SdÅ1 iÆ1 Si contenant 0 dans son enveloppe convexe, i.e. un sous-ensemble T tel que jT \Si j • 1 pour tout i et tel que 0 2 conv(T ). Ce théorème a donné naissance à de nombreuses questions, certaines algorithmiques et d’autres plus combinatoires. Dans ce manuscrit, nous nous intéressons à ces deux aspects. En 1997, Bárány et Onn ont défini la programmation linéaire colorée comme l’ensemble des questions algorithmiques liées au théorème de Carathéodory coloré. Parmi ces questions, deux ont particulièrement retenu notre attention. La première concerne la complexité du calcul d’un sous-ensemble arc-en-ciel comme dans l’énoncé du théorème. La seconde, en un sens plus générale, concerne la complexité du problème de décision suivant. Etant donnés des ensembles de points dans Rd , correspondant aux couleurs, il s’agit de décider s’il existe un sous-ensemble arc-en-ciel contenant 0 dans son enveloppe convexe, et ce en dehors des conditions du théorème de Carathéodory coloré. L’objectif de cette thèse est de mieux délimiter les cas polynomiaux et les cas “difficiles” de la programmation linéaire colorée. Nous présentons de nouveaux résultats de complexités permettant effectivement de réduire l’ensemble des cas encore incertains. En particulier, des versions combinatoires du théorème de Carathéodory coloré sont présentées d’un point de vue algorithmique. D’autre part, nous montrons que le problème de calcul d’un équilibre de Nash dans un jeu bimatriciel peut être réduit polynomialement à la programmation linéaire coloré. En prouvant ce dernier résultat, nous montrons aussi comment l’appartenance des problèmes de complémentarité à la classe PPAD peut être obtenue à l’aide du lemme de Sperner. Enfin, nous proposons une variante de l’algorithme de Bárány et Onn, calculant un sous ensemble arc-en-ciel contenant 0 dans son enveloppe convexe sous les conditions du théorème de Carathéodory coloré. Notre algorithme est clairement relié à l’algorithme du simplexe. Après une légère modification, il coïncide également avec l’algorithme de Lemke, calculant un équilibre de Nash dans un jeu bimatriciel. La question combinatoire posée par le théorème de Carathéodory coloré concerne le nombre de sous-ensemble arc-en-ciel contenant 0 dans leurs enveloppes convexes. Deza, Huang, Stephen et Terlaky (Colourful simplicial depth, Discrete Comput. Geom., 35, 597–604 (2006)) ont formulé la conjecture suivante. Si jSi j Æ d Å1 pour tout i 2 {1, . . . ,d Å1}, alors il y a au moins d2Å1 sous-ensemble arc-en-ciel contenant 0 dans leurs enveloppes convexes. Nous prouvons cette conjecture à l’aide d’objets combinatoires, connus sous le nom de systèmes octaédriques, dont nous présentons une étude plus approfondie<br>The colorful Carathéodory theorem, proved by Bárány in 1982, states the following. Given d Å1 sets of points S1, . . . ,SdÅ1 µ Rd , each of them containing 0 in its convex hull, there exists a colorful set T containing 0 in its convex hull, i.e. a set T µ SdÅ1 iÆ1 Si such that jT \Si j • 1 for all i and such that 0 2 conv(T ). This result gave birth to several questions, some algorithmic and some more combinatorial. This thesis provides answers on both aspects. The algorithmic questions raised by the colorful Carathéodory theorem concern, among other things, the complexity of finding a colorful set under the condition of the theorem, and more generally of deciding whether there exists such a colorful set when the condition is not satisfied. In 1997, Bárány and Onn defined colorful linear programming as algorithmic questions related to the colorful Carathéodory theorem. The two questions we just mentioned come under colorful linear programming. This thesis aims at determining which are the polynomial cases of colorful linear programming and which are the harder ones. New complexity results are obtained, refining the sets of undetermined cases. In particular, we discuss some combinatorial versions of the colorful Carathéodory theorem from an algorithmic point of view. Furthermore, we show that computing a Nash equilibrium in a bimatrix game is polynomially reducible to a colorful linear programming problem. On our track, we found a new way to prove that a complementarity problem belongs to the PPAD class with the help of Sperner’s lemma. Finally, we present a variant of the “Bárány-Onn” algorithm, which is an algorithmcomputing a colorful set T containing 0 in its convex hull whose existence is ensured by the colorful Carathéodory theorem. Our algorithm makes a clear connection with the simplex algorithm. After a slight modification, it also coincides with the Lemke method, which computes a Nash equilibriumin a bimatrix game. The combinatorial question raised by the colorful Carathéodory theorem concerns the number of positively dependent colorful sets. Deza, Huang, Stephen, and Terlaky (Colourful simplicial depth, Discrete Comput. Geom., 35, 597–604 (2006)) conjectured that, when jSi j Æ d Å1 for all i 2 {1, . . . ,d Å1}, there are always at least d2Å1 colourful sets containing 0 in their convex hulls. We prove this conjecture with the help of combinatorial objects, known as the octahedral systems. Moreover, we provide a thorough study of these objects

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Espinoza, Daniel G. "On Linear Programming, Integer Programming and Cutting Planes." Diss., Georgia Institute of Technology, 2006. http://hdl.handle.net/1853/10482.

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In this thesis we address three related topic in the field of Operations Research. Firstly we discuss the problems and limitation of most common solvers for linear programming, precision. We then present a solver that generate rational optimal solutions to linear programming problems by solving a succession of (increasingly more precise) floating point approximations of the original rational problem until the rational optimality conditions are achieved. This method is shown to be (on average) only 20% slower than the common pure floating point approach, while returning true optimal solutions to the problems. Secondly we present an extension of the Local Cut procedure introduced by Applegate et al, 2001, for the Symmetric Traveling Salesman Problem (STSP), to the general setting of MIP problems. This extension also proves finiteness of the separation, facet and tilting procedures in the general MIP setting, and also provides conditions under which the separation procedure is guaranteed to generate cuts that separate the current fractional solution from the convex hull of the mixed-integer polyhedron. We then move on to explore some configurations for local cuts, realizing extensive testing on the instances from MIPLIB. Those results show that this technique may be useful in general MIP problems, while the experience of Applegate et al, shows that the ideas can be successfully applied to structures problems as well. Thirdly we present an extensive computational experiment on the TSP and Domino Parity inequalities as introduced by Letchford, 2000. This work also include a safe-shrinking theorem for domino parity inequalities, heuristics to apply the planar separation algorithm introduced by Letchford to instances where the planarity requirement does not hold, and several practical speed-ups. Our computational experience showed that this class of inequalities effectively improve the lower bounds from the best relaxations obtained with Concorde, which is one of the state of the art solvers for the STSP. As part of these experience, we solved to optimality the (up to now) largest two STSP instances, both of them belong to the TSPLIB set of instances and they have 18,520 and 33,810 cities respectively.

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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. <br /><br /> 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<sup>-8</sup> when the machine precision on a 32-bit computer is approximately 10<sup>-16</sup>. <br /><br /> 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. <br /><br /> Finally, we present an algorithm to construct SDP problem instances with prescribed strict complementarity gaps. We then introduce two <em>measures of strict complementarity gaps</em>. 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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Wolf, Jan [Verfasser]. "Quantified Linear Programming / Jan Wolf." Aachen : Shaker, 2015. http://d-nb.info/1074087275/34.

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Sjöström, Henrik. "Pivoting methods for linear programming." Thesis, KTH, Matematik (Inst.), 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-98977.

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Price, C. J. "Non-linear semi-infinite programming." Thesis, University of Canterbury. Mathematics and Statistics, 1992. http://hdl.handle.net/10092/7920.

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Optimisation problems occur in many branches of science, engineering, and economics, as well as in other areas. The diversity of the various types of optimisation problems is extremely large, and so a unified approach is not attempted here. This thesis concentrates on a specific type of problem: non-linear semi-infinite programming.

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Wu, S. Y. "Linear programming on measure spaces." Thesis, University of Cambridge, 1985. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.372925.

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DIAS, DOUGLAS MOTA. "QUANTUM-INSPIRED LINEAR GENETIC PROGRAMMING." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2010. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=17544@1.

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COORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIOR<br>A superioridade de desempenho dos algoritmos quânticos, em alguns problemas específicos, reside no uso direto de fenômenos da mecânica quântica para realizar operações com dados em computadores quânticos. Esta característica fez surgir uma nova abordagem, denominada Computação com Inspiração Quântica, cujo objetivo é criar algoritmos clássicos (executados em computadores clássicos) que tirem proveito de princípios da mecânica quântica para melhorar seu desempenho. Neste sentido, alguns algoritmos evolutivos com inspiração quântica tem sido propostos e aplicados com sucesso em problemas de otimização combinatória e numérica, apresentando desempenho superior àquele dos algoritmos evolutivos convencionais, quanto à melhoria da qualidade das soluções e à redução do número de avaliações necessárias para alcançá-las. Até o presente momento, no entanto, este novo paradigma de inspiração quântica ainda não havia sido aplicado à Programação Genética (PG), uma classe de algoritmos evolutivos que visa à síntese automática de programas de computador. Esta tese propõe, desenvolve e testa um novo modelo de algoritmo evolutivo com inspiração quântica, denominado Programação Genética Linear com Inspiração Quântica (PGLIQ), para a evolução de programas em código de máquina. A Programação Genética Linear é assim denominada porque cada um dos seus indivíduos é representado por uma lista de instruções (estruturas lineares), as quais são executadas sequencialmente. As contribuições deste trabalho são o estudo e a formulação inédita do uso do paradigma da inspiração quântica na síntese evolutiva de programas de computador. Uma das motivações para a opção pela evolução de programas em código de máquina é que esta é a abordagem de PG que, por oferecer a maior velocidade de execução, viabiliza experimentos em larga escala. O modelo proposto é inspirado em sistemas quânticos multiníveis e utiliza o qudit como unidade básica de informação quântica, o qual representa a superposição dos estados de um sistema deste tipo. O funcionamento do modelo se baseia em indivíduos quânticos, que representam a superposição de todos os programas do espaço de busca, cuja observação gera indivíduos clássicos e os programas (soluções). Nos testes são utilizados problemas de regressão simbólica e de classificação binária para se avaliar o desempenho da PGLIQ e compará-lo com o do modelo AIMGP (Automatic Induction of Machine Code by Genetic Programming), considerado atualmente o modelo de PG mais eficiente na evolução de código de máquina, conforme citado em inúmeras referências bibliográficas na área. Os resultados mostram que a Programação Genética Linear com Inspiração Quântica (PGLIQ) apresenta desempenho geral superior nestas classes de problemas, ao encontrar melhores soluções (menores erros) a partir de um número menor de avaliações, com a vantagem adicional de utilizar um número menor de parâmetros e operadores que o modelo de referência. Nos testes comparativos, o modelo mostra desempenho médio superior ao do modelo de referência para todos os estudos de caso, obtendo erros de 3 a 31% menores nos problemas de regressão simbólica, e de 36 a 39% nos problemas de classificação binária. Esta pesquisa conclui que o paradigma da inspiração quântica pode ser uma abordagem competitiva para se evoluir programas eficientemente, encorajando o aprimoramento e a extensão do modelo aqui apresentado, assim como a criação de outros modelos de programação genética com inspiração quântica.<br>The superior performance of quantum algorithms in some specific problems lies in the direct use of quantum mechanics phenomena to perform operations with data on quantum computers. This feature has originated a new approach, named Quantum-Inspired Computing, whose goal is to create classic algorithms (running on classical computers) that take advantage of quantum mechanics principles to improve their performance. In this sense, some quantum-inspired evolutionary algorithms have been proposed and successfully applied in combinatorial and numerical optimization problems, presenting a superior performance to that of conventional evolutionary algorithms, by improving the quality of solutions and reducing the number of evaluations needed to achieve them. To date, however, this new paradigm of quantum inspiration had not yet been applied to Genetic Programming (GP), a class of evolutionary algorithms that aims the automatic synthesis of computer programs. This thesis proposes, develops and tests a novel model of quantum-inspired evolutionary algorithm named Quantum-Inspired Linear Genetic Programming (QILGP) for the evolution of machine code programs. Linear Genetic Programming is so named because each of its individuals is represented by a list of instructions (linear structures), which are sequentially executed. The contributions of this work are the study and formulation of the novel use of quantum inspiration paradigm on evolutionary synthesis of computer programs. One of the motivations for choosing by the evolution of machine code programs is because this is the GP approach that, by offering the highest speed of execution, makes feasible large-scale experiments. The proposed model is inspired on multi-level quantum systems and uses the qudit as the basic unit of quantum information, which represents the superposition of states of such a system. The model’s operation is based on quantum individuals, which represent a superposition of all programs of the search space, whose observation leads to classical individuals and programs (solutions). The tests use symbolic regression and binary classification problems to evaluate the performance of QILGP and compare it with the AIMGP model (Automatic Induction of Machine Code by Genetic Programming), which is currently considered the most efficient GP model to evolve machine code, as cited in numerous references in this field. The results show that Quantum-Inspired Linear Genetic Programming (QILGP) presents superior overall performance in these classes of problems, by achieving better solutions (smallest error) from a smaller number of evaluations, with the additional advantage of using a smaller number of parameters and operators that the reference model. In comparative tests, the model shows average performance higher than that of the reference model for all case studies, achieving errors 3-31% lower in the problems of symbolic regression, and 36-39% in the binary classification problems. This research concludes that the quantum inspiration paradigm can be a competitive approach to efficiently evolve programs, encouraging the improvement and extension of the model presented here, as well as the creation of other models of quantum-inspired genetic programming.

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Ramadan, Khaled Carleton University Dissertation Mathematics and Statistics. "Linear programming with interval coefficients." Ottawa, 1996.

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Books on the topic "Linear programming"

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Darst, Richard B. Introduction to linear programming: Applications and extensions. New York: M. Dekker, 1991.

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Karloff, Howard. Linear Programming. Boston, MA: Birkhäuser Boston, 1991. http://dx.doi.org/10.1007/978-0-8176-4844-2.

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Saigal, Romesh. Linear Programming. Boston, MA: Springer US, 1995. http://dx.doi.org/10.1007/978-1-4615-2311-6.

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Vanderbei, Robert J. Linear Programming. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-39415-8.

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Vanderbei, Robert J. Linear Programming. Boston, MA: Springer US, 2014. http://dx.doi.org/10.1007/978-1-4614-7630-6.

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Vanderbei, Robert J. Linear Programming. Boston, MA: Springer US, 2001. http://dx.doi.org/10.1007/978-1-4757-5662-3.

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Vanderbei, Robert J. Linear Programming. Boston, MA: Springer US, 2008. http://dx.doi.org/10.1007/978-0-387-74388-2.

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Ignizio, James P. Linear programming. Englewood Cliffs, N.J: Prentice Hall, 1994.

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Wisniewski, Mik. Linear programming. Basingstoke: Palgrave, 2001.

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Feiring, Bruce. Linear Programming. 2455 Teller Road, Thousand Oaks California 91320 United States of America: SAGE Publications, Inc., 1986. http://dx.doi.org/10.4135/9781412984751.

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Book chapters on the topic "Linear programming"

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Luc, Dinh The. "Linear Programming." In Multiobjective Linear Programming, 49–82. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-21091-9_3.

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Bhatti, M. Asghar. "Linear Programming." In Practical Optimization Methods, 315–436. New York, NY: Springer New York, 2000. http://dx.doi.org/10.1007/978-1-4612-0501-2_6.

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Blum, Lenore, Felipe Cucker, Michael Shub, and Steve Smale. "Linear Programming." In Complexity and Real Computation, 275–96. New York, NY: Springer New York, 1998. http://dx.doi.org/10.1007/978-1-4612-0701-6_15.

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Poler, Raúl, Josefa Mula, and Manuel Díaz-Madroñero. "Linear Programming." In Operations Research Problems, 1–48. London: Springer London, 2013. http://dx.doi.org/10.1007/978-1-4471-5577-5_1.

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Holden, K., and A. W. Pearson. "Linear Programming." In Introductory Mathematics for Economics and Business, 297–318. London: Macmillan Education UK, 1992. http://dx.doi.org/10.1007/978-1-349-22357-2_8.

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Čepin, Marko. "Linear Programming." In Assessment of Power System Reliability, 249–52. London: Springer London, 2011. http://dx.doi.org/10.1007/978-0-85729-688-7_16.

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Shimizu, Kiyotaka, Yo Ishizuka, and Jonathan F. Bard. "Linear Programming." In Nondifferentiable and Two-Level Mathematical Programming, 128–87. Boston, MA: Springer US, 1997. http://dx.doi.org/10.1007/978-1-4615-6305-1_5.

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Diwekar, Urmila. "Linear Programming." In Introduction to Applied Optimization, 1–29. Boston, MA: Springer US, 2008. http://dx.doi.org/10.1007/978-0-387-76635-5_2.

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Florenzano, Monique, and Cuong Le Van. "Linear Programming." In Studies in Economic Theory, 51–71. Berlin, Heidelberg: Springer Berlin Heidelberg, 2001. http://dx.doi.org/10.1007/978-3-642-56522-9_4.

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Woodford, C., and C. Phillips. "Linear Programming." In Numerical Methods with Worked Examples: Matlab Edition, 135–67. Dordrecht: Springer Netherlands, 2012. http://dx.doi.org/10.1007/978-94-007-1366-6_7.

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Conference papers on the topic "Linear programming"

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Kasperski, Adam, and Paweł Zieliński. "Recoverable Possibilistic Linear Programming." In 2024 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), 1–8. IEEE, 2024. http://dx.doi.org/10.1109/fuzz-ieee60900.2024.10612017.

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Flanagan, Mark F. "Linear-programming receivers." In 2008 46th Annual Allerton Conference on Communication, Control, and Computing. IEEE, 2008. http://dx.doi.org/10.1109/allerton.2008.4797568.

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Banzhaf, Wolfgang, and Ting Hu. "Linear Genetic Programming." In GECCO '24 Companion: Genetic and Evolutionary Computation Conference Companion, 759–71. New York, NY, USA: ACM, 2024. http://dx.doi.org/10.1145/3638530.3648422.

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Xu, Zhiming, Yu Bai, and Shuning Wang. "Sequential Global Linear Programming Algorithm for Continuous Piecewise Linear Programming*." In 2018 13th World Congress on Intelligent Control and Automation (WCICA). IEEE, 2018. http://dx.doi.org/10.1109/wcica.2018.8630336.

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Paolini, Luca, and Mauro Piccolo. "Semantically linear programming languages." In the 10th international ACM SIGPLAN symposium. New York, New York, USA: ACM Press, 2008. http://dx.doi.org/10.1145/1389449.1389462.

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Vaidya, Jaideep. "Privacy-preserving linear programming." In the 2009 ACM symposium. New York, New York, USA: ACM Press, 2009. http://dx.doi.org/10.1145/1529282.1529729.

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Taghavi, Mohammad, and Paul Siegel. "Adaptive Linear Programming Decoding." In 2006 IEEE International Symposium on Information Theory. IEEE, 2006. http://dx.doi.org/10.1109/isit.2006.262071.

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Ramos, Edgar A. "Linear programming queries revisited." In the sixteenth annual symposium. New York, New York, USA: ACM Press, 2000. http://dx.doi.org/10.1145/336154.336198.

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Yang, Jihui. "Fuzzy relation linear programming." In 2009 IEEE International Conference on Granular Computing (GRC). IEEE, 2009. http://dx.doi.org/10.1109/grc.2009.5255037.

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Ghosh, Arka, Piotr Hofman, and Sławomir Lasota. "Orbit-finite linear programming." In 2023 38th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS). IEEE, 2023. http://dx.doi.org/10.1109/lics56636.2023.10175799.

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Reports on the topic "Linear programming"

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Bixby, Robert E. Linear Programming Tools for Integer Programming. Fort Belvoir, VA: Defense Technical Information Center, October 1989. http://dx.doi.org/10.21236/ada219013.

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Bixby, Robert. Linear-Programming Tools in Integer Programming: The Traveling Salesman. Fort Belvoir, VA: Defense Technical Information Center, October 1992. http://dx.doi.org/10.21236/ada261398.

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Klotz, Edward S. Dynamic Pricing Criteria in Linear Programming. Fort Belvoir, VA: Defense Technical Information Center, July 1988. http://dx.doi.org/10.21236/ada198945.

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Quinn, J. J., R. L. Johnson, and L. A. Durham. Optimized groundwater containment using linear programming. Office of Scientific and Technical Information (OSTI), July 1998. http://dx.doi.org/10.2172/656456.

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Gill, Philip E., Walter Murray, Dulce B. Ponceleon, and Michael A. Saunders. Primal-Dual Methods for Linear Programming. Fort Belvoir, VA: Defense Technical Information Center, May 1991. http://dx.doi.org/10.21236/ada237418.

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Ebeida, Mohamed, Ahmed Abdelkader, Nina Amenta, Drew Kouri, Ojas Parekh, Cynthia Phillips, and Nickolas Winovich. Novel Geometric Operations for Linear Programming. Office of Scientific and Technical Information (OSTI), November 2020. http://dx.doi.org/10.2172/1813669.

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Gearhart, Jared Lee, Kristin Lynn Adair, Justin David Durfee, Katherine A. Jones, Nathaniel Martin, and Richard Joseph Detry. Comparison of open-source linear programming solvers. Office of Scientific and Technical Information (OSTI), October 2013. http://dx.doi.org/10.2172/1104761.

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Murray, W., and M. A. Saunders. New approaches to linear and nonlinear programming. Office of Scientific and Technical Information (OSTI), March 1990. http://dx.doi.org/10.2172/5254075.

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Todd, Michael J., and Yinyu Ye. A Centered Projective Algorithm for Linear Programming. Fort Belvoir, VA: Defense Technical Information Center, February 1988. http://dx.doi.org/10.21236/ada192100.

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Domich, Paul D., Paul T. Boggs, Janet R. Donaldson, and Christoph Witzgall. Optimal 3-dimensional methods for linear programming. Gaithersburg, MD: National Institute of Standards and Technology, 1989. http://dx.doi.org/10.6028/nist.ir.89-4225.

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