On well-posedness associated with a class of controlled variational inequalities

Savin Treanţă,Shalini Jha

doi:10.1051/mmnp/2021046

Abstract

In this paper, by using the new concepts of monotonicity, pseudomonotonicity and hemicontinuity associated with the considered curvilinear integral functional, we investigate the well-posedness and well-posedness in generalized sense for a class of controlled variational inequality problems. More precisely, by introducing the approximating solution set of the considered class of controlled variational inequality problems, we formulate and prove some characterization results on well-posedness and well-posedness in generalized sense. Also, the theoretical developments presented in the paper are accompanied by illustrative examples.

Highlights

The concept of well-posedness has significant role in the stability theory of optimization problems, which has been discussed in different areas of optimization likewise calculus of variations, mathematical programming, and optimal control
By using the new concepts of monotonicity, pseudomonotonicity and hemicontinuity associated with the considered curvilinear integral functional, and the approximating solution set of the considered class of controlled variational inequality problems, we formulate and prove some characterization results on well-posedness and well-posedness in generalized sense
In order to investigate the well-posedness and well-posedness in generalized sense of (CVIP), we introduce the definition of approximating solution set of (CVIP) as follows: Θι =

Summary

Introduction

The concept of well-posedness has significant role in the stability theory of optimization problems, which has been discussed in different areas of optimization likewise calculus of variations, mathematical programming, and optimal control This notion is important for problems due to certainty of the existence of the solution. By using the new concepts of monotonicity, pseudomonotonicity and hemicontinuity associated with the considered curvilinear integral functional, and the approximating solution set of the considered class of controlled variational inequality problems, we formulate and prove some characterization results on well-posedness and well-posedness in generalized sense.

Notations and preliminaries

Conclusions