Mathematical Programming with System of Equilibrium Constraints
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In this paper, we study the mathematical program with system of equilibrium constraints. This problem contains bilevel program with system of equilibrium constraints, semi-infinite program with system of equilibrium constraints, mathematical program with Nash equilibrium constraints, mathematical program with system of mixed variational like inequalities constraints. We establish the existence theorems of mathematical program with system of equilibrium constraints under various assumptions.
KeywordsMathematical program (resp. bilevel problem, semi-infinite problem) with system of equilibrium constraints Concave (resp. convex) multivalued map Upper (resp. lower) semicontinuous multivalued map
- Aubin J.P., Cellina A. (1994) Differential Inclusion. Springer Verlag, Berlin, GermanyGoogle Scholar
- Bard J.F. (1998) Pratical Bilevel Optimization, Algorithms and Applications, Nonconvex Optimization and its Applications. Kluwer Academic Publishers, DordrechltGoogle Scholar
- Luo Z.Q., Pang J.S., Ralph D. (1997) Mathematical Program with Equilibrium Constraint. Cambridge University Press, CambridgeGoogle Scholar
- Stein O. (2003) Bilevel Strategies in Semi-infinite Programming. Kluwer Academy publishers, DordrechtGoogle Scholar