Sensitivity of Optimal Solutions to Control Problems for Second Order Evolution Subdifferential Inclusions

Krzysztof Bartosz; Zdzisław Denkowski; Piotr Kalita

doi:10.1007/s00245-014-9262-4

Sensitivity of Optimal Solutions to Control Problems for Second Order Evolution Subdifferential Inclusions

Appl Math Optim. 2015;71(3):379-410. doi: 10.1007/s00245-014-9262-4.

Authors

Krzysztof Bartosz¹, Zdzisław Denkowski¹, Piotr Kalita¹

Affiliation

¹ Institute of Computer Science, Faculty of Mathematics and Computer Science, Jagiellonian University, ul. Łojasiewicza 6, 30-348 Kraków, Poland.

Abstract

In this paper the sensitivity of optimal solutions to control problems described by second order evolution subdifferential inclusions under perturbations of state relations and of cost functionals is investigated. First we establish a new existence result for a class of such inclusions. Then, based on the theory of sequential [Formula: see text]-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 the state relations and some complementary [Formula: see text]-convergence of the cost functionals. Then these two properties are implemented in the considered case.

Keywords: Control problem; Evolution subdifferential inclusion; Multifunction; Pseudomonotone and maximal monotone operators; Sensitivity; The Clarke subdifferential; [Formula: see text]- and [Formula: see text]-convergences.