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dc.contributor.authorZheng, X.
dc.contributor.authorSun, X.
dc.contributor.authorLi, D.
dc.contributor.authorSun, Jie
dc.date.accessioned2017-01-30T13:57:18Z
dc.date.available2017-01-30T13:57:18Z
dc.date.created2015-04-09T09:08:03Z
dc.date.issued2014
dc.identifier.citationZheng, X. and Sun, X. and Li, D. and Sun, J. 2014. Successive Convex Approximations to Cardinality-Constrained Convex Programs: A Piecewise-Linear DC Approach. Computational Optimization and Applications. 59 (1): pp. 379-397.
dc.identifier.urihttp://hdl.handle.net/20.500.11937/36727
dc.identifier.doi10.1007/s10589-013-9582-3
dc.description.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 convexfunctions) 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.

dc.publisherKluwer Academic Publishers
dc.subjectCardinality constraint
dc.subjectConvex programs
dc.subjectStrengthening cuts
dc.subjectSuccessive convex approximation
dc.subjectDC approximation
dc.subjectPortfolio selection
dc.titleSuccessive Convex Approximations to Cardinality-Constrained Convex Programs: A Piecewise-Linear DC Approach
dc.typeJournal Article
dcterms.source.volume59
dcterms.source.number1
dcterms.source.startPage379
dcterms.source.endPage397
dcterms.source.issn0926-6003
dcterms.source.titleComputational Optimization and Applications
curtin.note

The final publication is available at Springer via http://doi.org/10.1007/s10589-013-9582-3.

curtin.accessStatusOpen access


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