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Computational Optimization and Applications

, Volume 59, Issue 1–2, pp 379–397 | Cite as

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

  • Xiaojin Zheng
  • Xiaoling Sun
  • Duan Li
  • Jie Sun
Article

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.

Keywords

Convex programs Cardinality constraint DC approximation Successive convex approximation Strengthening cuts Portfolio selection 

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.School of Economics and ManagementTongji UniversityShanghaiP.R. China
  2. 2.Department of Management Science, School of ManagementFudan UniversityShanghaiP.R. China
  3. 3.Department of Systems Engineering and Engineering ManagementThe Chinese University of Hong KongShatinHong Kong
  4. 4.Department of Decision Sciences and Risk Management InstituteNational University of SingaporeSingaporeSingapore

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