Optimization problems with quasi-variational inequality constraints
The main aim of the contribution is to propose a numerical method for the optimization problems with parameter-dependent Quasi-Variational Inequalities (QVI) or Implicit Complementarity Problems (ICP) as side constraints. Thereby we confine ourselves to the simpler case in which the solutions of QVI (ICP) are unique (or at least locally unique) and depend on the parameter in a lipschitzian way. In the first part we state the problem and give some motivating examples coming from mechanics. The second part deals with the numerical solution of QVI (ICP) for fixed values of the parameter by a nonsmooth variant of the Newton method, which has shown a surprising effectiveness in the applications being considered. In particular, we show that the appropriate operators are semismooth and discuss the nonsingularity condition. The third part is devoted to our optimization problems which are cast in such a way that the bundle techniques from nonsmooth optimization can be applied. To compute the needed {open_quotes}subgradient{close_quotes} information, we characterize the maps, assigning to the single admissible values of the parameter the corresponding solution of the QVI, by generalized Jacobians. As a test example, the optimal covering problem from shape optimization is taken, in which the rigid obstacle is replaced by an elastic one.
- OSTI ID:
- 36355
- Report Number(s):
- CONF-9408161-; TRN: 94:009753-0695
- Resource Relation:
- Conference: 15. international symposium on mathematical programming, Ann Arbor, MI (United States), 15-19 Aug 1994; Other Information: PBD: 1994; Related Information: Is Part Of Mathematical programming: State of the art 1994; Birge, J.R.; Murty, K.G. [eds.]; PB: 312 p.
- Country of Publication:
- United States
- Language:
- English
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