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The stable duality of DC programs for composite convex functions. (English) Zbl 1365.90218

Summary: In this paper, we consider a composite DC optimization problem with a cone-convex system in locally convex Hausdorff topological vector spaces. By using the properties of the epigraph of the conjugate functions, some necessary and sufficient conditions which characterize the strong Fenchel-Lagrange duality and the stable strong Fenchel-Lagrange duality are given. We apply the results obtained to study the minmax optimization problem and \(l_1\) penalty problem.

MSC:

90C26 Nonconvex programming, global optimization
90C30 Nonlinear programming
90C46 Optimality conditions and duality in mathematical programming
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