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The Toland-Fenchel-Lagrange duality of DC programs for composite convex functions

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  • In this paper, by virtue of the epigraph technique, we construct a new kind of closedness-type constraint qualification, which is the sufficient and necessary condition to guarantee the strong duality between a cone constraint composite optimization problem and its dual problem holds. Under this closedness-type constraint qualification condition, we obtain a formula of subdifferential for composite functions and study a cone constraint composite DC optimization problem in locally convex Hausdorff topological vector spaces.
    Mathematics Subject Classification: Primary: 90C26, 90C46; Secondary: 90C30.

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