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2014•Abstract and Applied AnalysisOpen access

A Note on Optimality Conditions for DC Programs Involving Composite Functions

Xiangkai Sun, Hongyong Fu

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Abstract

By using the formula of theε-subdifferential for the sum of a convex function with a composition of convex functions, some necessary and sufficient optimality conditions for a DC programming problem involving a composite function are obtained. As applications, a composed convex optimization problem, a DC optimization problem, and a convex optimization problem with a linear operator are examined at the end of this paper.

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What this paper is about

By using the formula of theε-subdifferential for the sum of a convex function with a composition of convex functions, some necessary and sufficient optimality conditions for a DC programming problem involving a composite function are obtained. As applications, a composed convex optimization problem, a DC optimization problem, and a convex optimization problem with a linear operator are examined at the end of this paper.

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Available abstract

By using the formula of theε-subdifferential for the sum of a convex function with a composition of convex functions, some necessary and sufficient optimality conditions for a DC programming problem involving a composite function are obtained. As applications, a composed convex optimization problem, a DC optimization problem, and a convex optimization problem with a linear operator are examined at the end of this paper.

Key concepts: Subderivative, Mathematics, Convex optimization, Operator (biology), Proper convex function, Conic optimization, Convex analysis, Convex function

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