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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.

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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