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Necessary optimality conditions for optimization problems with variational inequality constraints. (English) Zbl 1088.90042
By use of Mordukhovich’s coderivative for set-valued mappings [cf. B. S. Mordukhovich, J. Math. Anal. Appl. 183, No. 1, 250–288 (1994; Zbl 0807.49016)], necessary optimality conditions of Karush-Kuhn-Tucker type for mathematical programming problems with equilibrium constraints are derived. The main assumption used to obtain this result is that the solution set mapping of a parametric generalized equation corresponding to the variational inequality constraint is pseudo-upper-Lipschitz continuous. It is shown that this necessary optimality condition is valid for bilevel optimization problems with parametric quadratic optimization problems in the lower level without any constraint qualifications.

MSC:
90C26 Nonconvex programming, global optimization
90C46 Optimality conditions and duality in mathematical programming
49K99 Optimality conditions
91A65 Hierarchical games (including Stackelberg games)
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