Necessary Optimality Conditions for Vector Reverse Convex Minimization Problems via a Conjugate Duality

In this paper, we are concerned with a vector reverse convex minimization problem ( P ) . For such a problem, by means of the so-called Fenchel–Lagrange duality, we provide necessary optimality conditions for proper efficiency in the sense of Geoffrion. This duality is used after a decomposition of...

Full description

Saved in:
Bibliographic Details
Published in:Vietnam journal of mathematics Vol. 52; no. 1; pp. 265 - 282
Main Authors: Keraoui, Houda, Aboussoror, Abdelmalek
Format: Journal Article
Language:English
Published: Singapore Springer Nature Singapore 01.03.2024
Springer Nature B.V
Subjects:
Banach spaces
Convex analysis
Convexity
Decomposition
Mathematics
Mathematics and Statistics
Optimization
Original Article
Optimality conditions
Secondary: 90C26
90C46
Primary: 90C29
90C25
Multiobjective programming
Reverse convex programming
Convex programming
ISSN:2305-221X, 2305-2228
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In this paper, we are concerned with a vector reverse convex minimization problem ( P ) . For such a problem, by means of the so-called Fenchel–Lagrange duality, we provide necessary optimality conditions for proper efficiency in the sense of Geoffrion. This duality is used after a decomposition of problem ( P ) into a family of convex vector minimization subproblems and scalarization of these subproblems. The optimality conditions are expressed in terms of subdifferentials and normal cones in the sense of convex analysis. The obtained results are new in the literature of vector reverse convex programming. Moreover, some of them extend with improvement some similar results given in the literature, from the scalar case to the vectorial one.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:2305-221X
2305-2228
DOI:10.1007/s10013-022-00602-2