A nonsmooth approach to optimization problems with equilibrium constraints. (English) Zbl 0887.90168

Kočvara, Michal; Outrata, Jiří V.

Ferris, Michael C. (ed.) et al., Complementarity and variational problems. State of the art. Proceedings of the international conference, Baltimore, MD, USA, November 1–4, 1995. Philadelphia, PA: SIAM, Society for Industrial and Applied Mathematics. 148-164 (1997).

The authors consider a class of optimization problems in which either nonlinear complementarity or implicit complementarity problems arise as side constraints. Under the assumption of strong regularity of Robinson at a local minimum, the authors derive necessary optimality conditions and propose a numerical approach to the solution of these problems. This approach is applied to a design problem from continuum mechanics.
For the entire collection see [Zbl 0863.00054].

Reviewer: P.Neittaanmäki (Jyväskylä)

MSC:

90C33	Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
90C31	Sensitivity, stability, parametric optimization
90C30	Nonlinear programming
49J52	Nonsmooth analysis

Keywords:

bilevel programming; generalized Jacobian; necessary optimality conditions; continuum mechanics; strong regularity