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...

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Vydáno v:Vietnam journal of mathematics Ročník 52; číslo 1; s. 265 - 282
Hlavní autoři: Keraoui, Houda, Aboussoror, Abdelmalek
Médium: Journal Article
Jazyk:angličtina
Vydáno: Singapore Springer Nature Singapore 01.03.2024
Springer Nature B.V
Témata:
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
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Shrnutí: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.
Bibliografie:ObjectType-Article-1
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ISSN:2305-221X
2305-2228
DOI:10.1007/s10013-022-00602-2