Necessary and sufficient conditions of optimality for second order discrete and differential inequalities-Reference-Cited by-同舟云学术

Necessary and sufficient conditions of optimality for second order discrete and differential inequalities

Published:2022-01-23 Issue:3 Volume:29 Page:407-424
ISSN:1072-947X
Container-title:Georgian Mathematical Journal
language:en
Short-container-title:

Author:

Mahmudov Elimhan N.¹^ORCID,Demir Sağlam Sevilay²^ORCID

Affiliation:

1. Department of Mathematics , Istanbul Technical University , Istanbul , Turkey ; and Azerbaijan National Academy of Sciences, Institute of Control Systems, Baku, Azerbaijan

2. Department of Mathematics , Istanbul University , Istanbul , Turkey

Abstract

Abstract The present paper studies the optimization of the Bolza problem with a system of convex and nonconvex, discrete and differential state variable second-order inequality constraints by deriving necessary and sufficient conditions of optimality. The problem with a system of discrete-approximation inequalities is investigated using the proposed method of discretization and equivalence theorems for subdifferential inclusions, which greatly contributes to the derivation of adjoint discrete inclusions generated by a given system of nonlinear inequality constraints. Furthermore, we formulate sufficient conditions of optimality for the continuous problem by passing to the case of limit. A numerical example is provided to illustrate the theoretical approach’s effectiveness.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/gmj-2021-2134/pdf

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