Necessary and Sufficient Optimality Conditions for Non-regular Problems

V. Vivanco-Orellana; R. Osuna-Gómez; M. A. Rojas-Medar

doi:10.1080/01630563.2023.2235614

Necessary and Sufficient Optimality Conditions for Non-regular Problems

V. Vivanco-Orellana
, R. Osuna-Gómez
, M. A. Rojas-Medar

Department of Mathematics

Universidad Católica de la Santísima Concepción
University of Seville

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

We derive new necessary and sufficient optimality conditions for optimization problems with multi-equality and inequality constraints through the Dubovitskii-Milyutin formalism, characterizing the feasible and tangent directions cones in a neighborhood of a non-regular point. We also establish conditions of 2-regularity under which necessary optimality conditions are non-degenerate. These conditions apply when the phenomenon of non-regularity (or abnormality) take place. In addition examples that illustrate our results are presented.

Original language	English
Pages (from-to)	1228-1250
Number of pages	23
Journal	Numerical Functional Analysis and Optimization
Volume	44
Issue number	12
DOIs	https://doi.org/10.1080/01630563.2023.2235614
State	Published - 2023

Keywords

Dubovitskii-Milyutin formalism
necessary and sufficient optimality conditions
non-regular optimization problem
tangent and feasible cones of second-order

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10.1080/01630563.2023.2235614

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abstract = "We derive new necessary and sufficient optimality conditions for optimization problems with multi-equality and inequality constraints through the Dubovitskii-Milyutin formalism, characterizing the feasible and tangent directions cones in a neighborhood of a non-regular point. We also establish conditions of 2-regularity under which necessary optimality conditions are non-degenerate. These conditions apply when the phenomenon of non-regularity (or abnormality) take place. In addition examples that illustrate our results are presented.",

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T1 - Necessary and Sufficient Optimality Conditions for Non-regular Problems

AU - Vivanco-Orellana, V.

AU - Osuna-Gómez, R.

AU - Rojas-Medar, M. A.

PY - 2023

Y1 - 2023

N2 - We derive new necessary and sufficient optimality conditions for optimization problems with multi-equality and inequality constraints through the Dubovitskii-Milyutin formalism, characterizing the feasible and tangent directions cones in a neighborhood of a non-regular point. We also establish conditions of 2-regularity under which necessary optimality conditions are non-degenerate. These conditions apply when the phenomenon of non-regularity (or abnormality) take place. In addition examples that illustrate our results are presented.

AB - We derive new necessary and sufficient optimality conditions for optimization problems with multi-equality and inequality constraints through the Dubovitskii-Milyutin formalism, characterizing the feasible and tangent directions cones in a neighborhood of a non-regular point. We also establish conditions of 2-regularity under which necessary optimality conditions are non-degenerate. These conditions apply when the phenomenon of non-regularity (or abnormality) take place. In addition examples that illustrate our results are presented.

KW - Dubovitskii-Milyutin formalism

KW - necessary and sufficient optimality conditions

KW - non-regular optimization problem

KW - tangent and feasible cones of second-order

UR - https://www.scopus.com/pages/publications/85166767033

U2 - 10.1080/01630563.2023.2235614

DO - 10.1080/01630563.2023.2235614

M3 - Article

AN - SCOPUS:85166767033

SN - 0163-0563

VL - 44

SP - 1228

EP - 1250

JO - Numerical Functional Analysis and Optimization

JF - Numerical Functional Analysis and Optimization

IS - 12

ER -

Necessary and Sufficient Optimality Conditions for Non-regular Problems

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Keywords

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