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

Yuying Zhou; Gang  Li

doi:10.3934/naco.2014.4.9

Article Contents

2014, Volume 4, Issue 1: 9-23. Doi: 10.3934/naco.2014.4.9

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

Yuying Zhou^1, and
Gang Li^2,

1.
Department of Mathematics, Soochow University, Suzhou, 215006
2.
School of Sciences, Zhejiang A & F University, Hangzhou 311300

Received: March 2013

Revised: October 2013

Published: November 2013

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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.

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Mathematics Subject Classification: Primary: 90C26, 90C46; Secondary: 90C30.

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