Duality and optimality conditions for reverse convex programs via a convex decomposition

In this paper via the so-called Fenchel–Lagrange duality, we provide necessary local optimality conditions for a reverse convex programming problem ( P ) . As is well known, this duality has been first defined for convex programming problems. So, since in general problem ( P ) is not convex even if...

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Bibliographic Details
Published in:Rendiconti del Circolo matematico di Palermo Vol. 72; no. 8; pp. 3917 - 3930
Main Authors: Keraoui, Houda, Fatajou, Samir, Aboussoror, Abdelmalek
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 01.12.2023
Subjects:
Algebra
Analysis
Applications of Mathematics
Geometry
Mathematics
Mathematics and Statistics
90C26
Conjugate duality
90C46
Reverse convex programs
90C25
Convex analysis
ISSN:0009-725X, 1973-4409
Online Access:Get full text
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Summary:In this paper via the so-called Fenchel–Lagrange duality, we provide necessary local optimality conditions for a reverse convex programming problem ( P ) . As is well known, this duality has been first defined for convex programming problems. So, since in general problem ( P ) is not convex even if the data is, we first proceed to a decomposition of an equivalent problem of ( P ) into a family of convex minimization subproblems. Then, by means of the decomposition and the Fenchel–Lagrange duality applied to the subproblems we provide necessary local optimality conditions for the initial problem  ( P ) .
ISSN:0009-725X
1973-4409
DOI:10.1007/s12215-023-00876-6