×

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

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.

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

Software:

NLPQL
PDF BibTeX XML Cite
Full Text: DOI