Outrata, Jiří V. On optimization problems with variational inequality constraints. (English) Zbl 0826.90114 SIAM J. Optim. 4, No. 2, 340-357 (1994). In a finite-dimensional space this paper studied a class of optimization problems subject to variational inequality constraints. In terms of results in nonsmooth analysis first-order necessary optimality conditions are derived for the cases that the set-valued mapping of the solution of the variational inequality constraints is differentiable or not differentiable. Under certain conditions the optimization problem can be rewritten as a nondifferentiable optimization problem. It is thus claimed that a nondifferentiable optimization technique can be used for computing the solution. It is pointed out, however, that the first-order necessary condition obtained may not, in general, be sufficient. Reviewer: X.Q.Yang (Nedlands) Cited in 28 Documents MSC: 90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming) 49J40 Variational inequalities 49J52 Nonsmooth analysis 90C31 Sensitivity, stability, parametric optimization Keywords:finite-dimensional space; variational inequality constraints; nonsmooth analysis; first-order necessary optimality conditions; nondifferentiable optimization Software:NLPQL PDF BibTeX XML Cite \textit{J. V. Outrata}, SIAM J. Optim. 4, No. 2, 340--357 (1994; Zbl 0826.90114) Full Text: DOI OpenURL