Well Posedness of New Optimization Problems with Variational Inequality Constraints

Savin Treanţă

doi:10.3390/fractalfract5030123

Savin Treanţă

Open Access

https://doi.org/10.3390/fractalfract5030123

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Journal: Fractal and Fractional	Publication Date: Sep 15, 2021
Citations: 7	License type: CC BY 4.0

Affiliation: Polytechnic University of Bucharest

Abstract

In this paper, we studied the well posedness for a new class of optimization problems with variational inequality constraints involving second-order partial derivatives. More precisely, by using the notions of lower semicontinuity, pseudomonotonicity, hemicontinuity and monotonicity for a multiple integral functional, and by introducing the set of approximating solutions for the considered class of constrained optimization problems, we established some characterization results on well posedness. Furthermore, to illustrate the theoretical developments included in this paper, we present some examples.

Highlights

Motivated by the aforementioned research works, in this paper we analyze the well posedness of a new class of constrained optimization problems governed by multiple integral functionals involving second-order partial derivatives
First we introduce new forms for the concepts of monotonicity, lower semicontinuity, pseudomonotonicity and hemicontinuity associated with a multiple integral functional
We investigated the well posedness for a new class of constrained optimization problems governed by second-order partial derivatives

Summary

Introduction

Motivated by the aforementioned research works, in this paper we analyze the well posedness of a new class of constrained optimization problems governed by multiple integral functionals involving second-order partial derivatives. To this aim, first we introduce new forms for the concepts of monotonicity, lower semicontinuity, pseudomonotonicity and hemicontinuity associated with a multiple integral functional. The main novelty elements of this paper are represented by the following: the mathematical framework is based on infinitedimensional function spaces, multiple integral functionals, the presence of second-order partial derivatives, and innovative proofs of the main results.

Preliminaries

Findings

Conclusions and Further Developments