Successive convex approximations to cardinality-constrained convex programs: a piecewise-linear DC approach

Xiaojin Zheng (), Xiaoling Sun (), Duan Li () and Jie Sun ()

Computational Optimization and Applications, 2014, vol. 59, issue 1, 379-397

Abstract: In this paper we consider cardinality-constrained convex programs that minimize a convex function subject to a cardinality constraint and other linear constraints. This class of problems has found many applications, including portfolio selection, subset selection and compressed sensing. We propose a successive convex approximation method for this class of problems in which the cardinality function is first approximated by a piecewise linear DC function (difference of two convex functions) and a sequence of convex subproblems is then constructed by successively linearizing the concave terms of the DC function. Under some mild assumptions, we establish that any accumulation point of the sequence generated by the method is a KKT point of the DC approximation problem. We show that the basic algorithm can be refined by adding strengthening cuts in the subproblems. Finally, we report some preliminary computational results on cardinality-constrained portfolio selection problems. Copyright Springer Science+Business Media New York 2014

Keywords: Convex programs; Cardinality constraint; DC approximation; Successive convex approximation; Strengthening cuts; Portfolio selection (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (5)

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DOI: 10.1007/s10589-013-9582-3

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