The Toland-Fenchel-Lagrange duality of DC programs for composite convex functions
Yuying Zhou, Gang Li · Numerical Algebra Control and Optimization · 2013
In this paper, by virtue of the epigraph technique, we construct a new kind of closedness-type constraintqualification, which is the sufficient and necessary condition to guarantee thestrong 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.