Numerical Algebra, Control and Optimization (NACO)

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

Pages: 9 - 23, Volume 4, Issue 1, March 2014      doi:10.3934/naco.2014.4.9

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Yuying Zhou - Department of Mathematics, Soochow University, Suzhou, 215006, China (email)
Gang Li - School of Sciences, Zhejiang A & F University, Hangzhou 311300, China (email)

Abstract: 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.

Keywords:  Epigraph, duality, composite, constraint qualification.
Mathematics Subject Classification:  Primary: 90C26, 90C46; Secondary: 90C30.

Received: March 2013;      Revised: October 2013;      Available Online: December 2013.