Sensitivity analysis of optimal control problems driven by dynamic history-dependent variational-hemivariational inequalities

Abstract

The aim of this paper is to investigate a nonlinear optimal control problem governed by a complicated dynamic variational-hemivariational inequality (DVHVI, for short) with history-dependent operators in the framework of an evolution triple of spaces. First, we prove a generalized existence and uniqueness theorem to a class of dynamic variational-hemivariational inequalities, which extends the recent results established by Han-Migórski-Sofonea [12, Theorem 9] and Migórski-Bai [23, Theorem 5]. Then, an optimal control problem driven by a (DVHVI) is studied and an existence theorem is delivered. Finally, we explore the sensitivity properties of the optimal control problem under the consideration depending on the initial data ξ∈H and some further parameter λ∈E.