Restricted Robinson Constraint Qualification and Optimality for Cardinality-Constrained Cone Programming

Lili Pan (), Ziyan Luo () and Naihua Xiu ()
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Lili Pan: Beijing Jiaotong University
Ziyan Luo: Beijing Jiaotong University
Naihua Xiu: Beijing Jiaotong University

Journal of Optimization Theory and Applications, 2017, vol. 175, issue 1, No 5, 104-118

Abstract: Abstract In this paper, optimality conditions are presented and analyzed for the cardinality-constrained cone programming arising from finance, statistical regression, signal processing, etc. By introducing a restricted form of (strict) Robinson constraint qualification, the first-order optimality conditions for the cardinality-constrained cone programming are established based upon the properties of the normal cone. After characterizing further the second-order tangent set to the cardinality-constrained system, the second-order optimality conditions are also presented under some mild conditions. These proposed optimality conditions, to some extent, enrich the optimization theory for noncontinuous and nonconvex programming problems.

Keywords: Cardinality constraint; Cone programming; Optimality condition; Constraint qualification; 90C26; 90C30; 90C46 (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10957-017-1166-4

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