Mathematical programming with equilibrium constraints: Difference between revisions
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==Introduction== | ==Introduction== | ||
A Mathematical Program with Equilibrium Constraint (MPEC) are special class of constrained optimization problems inside of nonlinear programming (NLP) [1]. These are constrained optimization problems where the constraints include equilibrium constraints like variational inequalities or complementary conditions. MPECs have applications in fields of engineering design, economic equilibrium, high level games, and modeling of transportation [2]. The feasible set of MPEC violates most of the standard constraint qualifications and are difficult to solve due to the feasible region not necessarily being convex or connected [1]. It is necessary to consider suitable optimality conditions for solving these optimization problems. Throughout this article, the theory and methodology behind MPEC will be discussed and an example will be given as well discussion on the applications pertaining to MPEC will occur. | |||
==Theory/Methodology/Algorithms== | ==Theory/Methodology/Algorithms== | ||
==At least one numerical example== | ==At least one numerical example== | ||
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==Conclusions== | ==Conclusions== | ||
==References== | ==References== | ||
[1] Joshi, B.C. Some Results on Mathematical Programs with Equilibrium Constraints. ''Oper. Res. Forum'' 2, 53 (2021). <nowiki>https://doi.org/10.1007/s43069-021-00061-4</nowiki> | |||
[2] M. Ferris, S. Dirkse, and A. Meeraus. Mathematical Programs with Equilibrium Constraints: Automatic Reformulation and Solution via Constrained Optimization. Northwestern University, Evanston, Illinois, July 2002. | |||
Revision as of 14:10, 24 November 2021
Authors: Andrew Amerman, Hannah Levy, Juan Henriquez, Matthew Baccaro, and Taha Shamshudin (SYSEN 5800 Fall 2021)
Introduction
A Mathematical Program with Equilibrium Constraint (MPEC) are special class of constrained optimization problems inside of nonlinear programming (NLP) [1]. These are constrained optimization problems where the constraints include equilibrium constraints like variational inequalities or complementary conditions. MPECs have applications in fields of engineering design, economic equilibrium, high level games, and modeling of transportation [2]. The feasible set of MPEC violates most of the standard constraint qualifications and are difficult to solve due to the feasible region not necessarily being convex or connected [1]. It is necessary to consider suitable optimality conditions for solving these optimization problems. Throughout this article, the theory and methodology behind MPEC will be discussed and an example will be given as well discussion on the applications pertaining to MPEC will occur.
Theory/Methodology/Algorithms
At least one numerical example
encouraged to have more than one
Applications
Conclusions
References
[1] Joshi, B.C. Some Results on Mathematical Programs with Equilibrium Constraints. Oper. Res. Forum 2, 53 (2021). https://doi.org/10.1007/s43069-021-00061-4
[2] M. Ferris, S. Dirkse, and A. Meeraus. Mathematical Programs with Equilibrium Constraints: Automatic Reformulation and Solution via Constrained Optimization. Northwestern University, Evanston, Illinois, July 2002.