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

Author

Listed:
  • Lili Pan

    (Beijing Jiaotong University
    Shandong University of Technology)

  • Ziyan Luo

    (Beijing Jiaotong University)

  • Naihua Xiu

    (Beijing Jiaotong University)

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.

Suggested Citation

  • Lili Pan & Ziyan Luo & Naihua Xiu, 2017. "Restricted Robinson Constraint Qualification and Optimality for Cardinality-Constrained Cone Programming," Journal of Optimization Theory and Applications, Springer, vol. 175(1), pages 104-118, October.
  • Handle: RePEc:spr:joptap:v:175:y:2017:i:1:d:10.1007_s10957-017-1166-4
    DOI: 10.1007/s10957-017-1166-4
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    References listed on IDEAS

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