Duality and optimality conditions for reverse convex programs via a convex decomposition - Keraoui, Houda; Fatajou, Samir; Aboussoror, Abdelmalek (Rendiconti del Circolo matematico di Palermo, 2023)
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 ) .