On optimization problems with variational inequality constraints. (English) Zbl 0826.90114

Outrata, Jiří V.

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)

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