|Sensitivity of Optimal Solutions to Control Problems for Systems Described by Hemivariational Inequalities|
Z. Denkowski, denkowski(at)softlab.ii.uj.edu.pl
S. Migórski, migorski(at)softlab.ii.uj.edu.pl
Jagiellonian University, Institute of Computer Science, Nawojki 11, 30-072 Cracow, Poland
Abstract: In this paper the sensitivity of optimal solutions to control problems for the systems described by stationary and evolution hemivariational inequalities (HVIs) under perturbations of state relations and of cost functionals is investigated. First, basing on the theory of sequential Γ-convergence we recall the abstract scheme concerning convergence of minimal values and minimizers. The abstract scheme works provided we can establish two properties: the Kuratowski convergence of solution sets for HVIs (state relations) and some complementary Γ-convergence of the cost functionals. Then these two properties are implemented in each considered case.
Keywords: Hemivariational inequality, control problem, sensitivity, the Clarke subdifferential, multifunction, pseudomonotone and maximal monotone operators, G, PG and Γ convergences.
Published in: Control and Cybernetics, vol. 33, no. 2 (2004), 211-236.