Ye, J. J.; Ye, X. Y. Necessary optimality conditions for optimization problems with variational inequality constraints. (English) Zbl 1088.90042 Math. Oper. Res. 22, No. 4, 977-997 (1997). 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. Reviewer: Stephan Dempe (MR 98m:90110) Cited in 97 Documents MSC: 90C26 Nonconvex programming, global optimization 90C46 Optimality conditions and duality in mathematical programming 49K99 Optimality conditions 91A65 Hierarchical games (including Stackelberg games) Citations:Zbl 0807.49016 PDF BibTeX XML Cite \textit{J. J. Ye} and \textit{X. Y. Ye}, Math. Oper. Res. 22, No. 4, 977--997 (1997; Zbl 1088.90042) Full Text: DOI Link OpenURL