Abstract
In this paper via the so-called Fenchel–Lagrange duality, we provide necessary local optimality conditions for a reverse convex programming problem \(({{\mathcal {P}}})\). As is well known, this duality has been first defined for convex programming problems. So, since in general problem \(({{\mathcal {P}}})\) is not convex even if the data is, we first proceed to a decomposition of an equivalent problem of \(({{\mathcal {P}}})\) 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 \(({{\mathcal {P}}})\).
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Keraoui, H., Fatajou, S. & Aboussoror, A. Duality and optimality conditions for reverse convex programs via a convex decomposition. Rend. Circ. Mat. Palermo, II. Ser 72, 3917–3930 (2023). https://doi.org/10.1007/s12215-023-00876-6
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DOI: https://doi.org/10.1007/s12215-023-00876-6