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Remarks on some variants of minimal point theorem and Ekeland variational principle with applications

Meghea Irina, Stamin Cristina Stefania

Demonstratio Mathematica

2022

Vol. 55, nr 1

354--379

This paper presents some variants of minimal point theorem together with corresponding variants of Ekeland variational principle. In the second part of this article, there is a discussion on Ekeland variational principle and minimal point theorem relative to it in uniform spaces. The aim of these series of important results is to highlight relations between them, some improvements and specific applications.

Sensitivity of optimal solutions to control problems for systems described by hemivariational inequalities

Denkowski Z., Migórski S.

Control and Cybernetics

2004

Vol. 33, no 2

211-236

In this paper the sensitivity of optimal solutions to control problems for the systems described by stationary and evolution heinivariational inequalities (HVIs) under perturbations of state relations and of cost functionals is investigated. First, basing on the theory of sequential [Gamma]-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 [Gamma]-convergence of the cost functionals. Then these two properties are implemented in each considered case.