The Experts below are selected from a list of 318 Experts worldwide ranked by ideXlab platform
I. R. De Farias - One of the best experts on this subject based on the ideXlab platform.
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Semi-continuous cuts for Mixed-Integer Programming
Lecture Notes in Computer Science, 2020Co-Authors: I. R. De FariasAbstract:We study the convex hull of the feasible set of the semi-continuous knapsack problem, in which the variables belong to the union of two intervals. Besides being important in its own right, the semi-continuous knapsack problem is a relaxation of general Mixed-Integer Programming. We show how strong inequalities that are valid for the semi-continuous knapsack polyhedron can be derived and used as cuts in a branch-and-cut scheme for Mixed-Integer Programming and problems with semi-continuous variables. We present computational results that demonstrate the effectiveness of these inequalities, which we call collectively semi-continuous cuts. Our computational experience also shows that dealing with semi-continuous constraints directly in the branch-and-cut algorithm through a specialized branching scheme and semi-continuous cuts is considerably more practical than the textbook approach of modeling semi-continuous constraints through the introduction of auxiliary binary variables in the model.
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IPCO - Semi-continuous Cuts for Mixed-Integer Programming
Integer Programming and Combinatorial Optimization, 2004Co-Authors: I. R. De FariasAbstract:We study the convex hull of the feasible set of the semi-continuous knapsack problem, in which the variables belong to the union of two intervals. Besides being important in its own right, the semi-continuous knapsack problem is a relaxation of general Mixed-Integer Programming. We show how strong inequalities that are valid for the semi-continuous knapsack polyhedron can be derived and used as cuts in a branch-and-cut scheme for Mixed-Integer Programming and problems with semi-continuous variables. We present computational results that demonstrate the effectiveness of these inequalities, which we call collectively semi-continuous cuts. Our computational experience also shows that dealing with semi-continuous constraints directly in the branch-and-cut algorithm through a specialized branching scheme and semi-continuous cuts is considerably more practical than the “textbook” approach of modeling semi-continuous constraints through the introduction of auxiliary binary variables in the model.
D. Acharya - One of the best experts on this subject based on the ideXlab platform.
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On a pair of nonlinear Mixed Integer Programming problems
European Journal of Operational Research, 2011Co-Authors: M.s. Mishra, D. Acharya, Sudarsan NandaAbstract:Abstract We consider maximin and minimax nonlinear Mixed Integer Programming problems which are nonsymmetric in duality sense. Under weaker (pseudo-convex/pseudo-concave) assumptions, we show that the supremum infimum of the maximin problem is greater than or equal to the infimum supremum of the minimax problem. As a particular case, this result reduces to the weak duality theorem for minimax and symmetric dual nonlinear Mixed Integer Programming problems. Further, this is used to generalize available results on minimax and symmetric duality in nonlinear Mixed Integer Programming.
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A note on a pair of nonlinear Mixed Integer Programming problems
European Journal of Operational Research, 2011Co-Authors: M.s. Mishra, Sudarsan Nanda, D. AcharyaAbstract:Abstract In a recent paper some duality results were proved for a pair of nonsymmetric and nonlinear Mixed Integer Programming problems under pseudo-convexity/pseudo-concavity, separability and an additional feasibility assumption. In this note the same results have been obtained under strong pseudoconvexity/strong pseudo-concavity and separability assumptions only.
Sudarsan Nanda - One of the best experts on this subject based on the ideXlab platform.
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On a pair of nonlinear Mixed Integer Programming problems
European Journal of Operational Research, 2011Co-Authors: M.s. Mishra, D. Acharya, Sudarsan NandaAbstract:Abstract We consider maximin and minimax nonlinear Mixed Integer Programming problems which are nonsymmetric in duality sense. Under weaker (pseudo-convex/pseudo-concave) assumptions, we show that the supremum infimum of the maximin problem is greater than or equal to the infimum supremum of the minimax problem. As a particular case, this result reduces to the weak duality theorem for minimax and symmetric dual nonlinear Mixed Integer Programming problems. Further, this is used to generalize available results on minimax and symmetric duality in nonlinear Mixed Integer Programming.
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A note on a pair of nonlinear Mixed Integer Programming problems
European Journal of Operational Research, 2011Co-Authors: M.s. Mishra, Sudarsan Nanda, D. AcharyaAbstract:Abstract In a recent paper some duality results were proved for a pair of nonsymmetric and nonlinear Mixed Integer Programming problems under pseudo-convexity/pseudo-concavity, separability and an additional feasibility assumption. In this note the same results have been obtained under strong pseudoconvexity/strong pseudo-concavity and separability assumptions only.
Laurence A Wolsey - One of the best experts on this subject based on the ideXlab platform.
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Wiley Encyclopedia of Computer Science and Engineering - Mixed Integer Programming
Wiley Encyclopedia of Computer Science and Engineering, 2008Co-Authors: Laurence A WolseyAbstract:A linear Mixed Integer program is an optimization problem in which a nonempty subset of Integer variables (unknowns) and a subset of real-valued (continuous) variables exist, the constraints are all linear equations or inequalities, and the objective is a linear function to be minimized (or maximized). After presenting several practical applications of Mixed Integer Programming, we describe the main classes of algorithms, branch-and-bound and branch-and-cut, that are used to solve this hard class of problems. Considerable attention is paid to ways to improve solution times, involving preprocessing, reformulation with cuts and/or new variables, and heuristics.
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production planning by Mixed Integer Programming
2006Co-Authors: Yves Pochet, Laurence A WolseyAbstract:This textbook provides a comprehensive modeling, reformulation and optimization approach for solving production planning and supply chain planning problems, covering topics from a basic introduction to planning systems, Mixed Integer Programming (MIP) models and algorithms through the advanced description of mathematical results in polyhedral combinatorics required to solve these problems. Based on twenty years worth of research in which the authors have played a significant role, the book addresses real life industrial production planning problems (involving complex production structures with multiple production stages) using MIP modeling and reformulation approach. The book provides an introduction to MIP modeling and to planning systems, a unique collection of reformulation results, and an easy to use problem-solving library. This approach is demonstrated through a series of real life case studies, exercises and detailed illustrations. Review by Jakub Marecek (Computer Journal) The emphasis put on Mixed Integer rounding and mixing sets, heuristics in-built in general purpose Integer Programming solvers, as well as on decompositions and heuristics using Integer Programming should be praised... There is no doubt that this volume offers the present best introduction to Integer Programming formulations of lotsizing problems, encountered in production planning. (2007)
M.s. Mishra - One of the best experts on this subject based on the ideXlab platform.
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On a pair of nonlinear Mixed Integer Programming problems
European Journal of Operational Research, 2011Co-Authors: M.s. Mishra, D. Acharya, Sudarsan NandaAbstract:Abstract We consider maximin and minimax nonlinear Mixed Integer Programming problems which are nonsymmetric in duality sense. Under weaker (pseudo-convex/pseudo-concave) assumptions, we show that the supremum infimum of the maximin problem is greater than or equal to the infimum supremum of the minimax problem. As a particular case, this result reduces to the weak duality theorem for minimax and symmetric dual nonlinear Mixed Integer Programming problems. Further, this is used to generalize available results on minimax and symmetric duality in nonlinear Mixed Integer Programming.
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A note on a pair of nonlinear Mixed Integer Programming problems
European Journal of Operational Research, 2011Co-Authors: M.s. Mishra, Sudarsan Nanda, D. AcharyaAbstract:Abstract In a recent paper some duality results were proved for a pair of nonsymmetric and nonlinear Mixed Integer Programming problems under pseudo-convexity/pseudo-concavity, separability and an additional feasibility assumption. In this note the same results have been obtained under strong pseudoconvexity/strong pseudo-concavity and separability assumptions only.
