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New Constraint Qualifications for Mathematical Programs with Second-Order Cone Complementarity Constraints

Author

Listed:
  • Yan-Chao Liang

    (Henan Normal University)

  • Yue-Wen Liu

    (Henan Normal University)

  • Gui-Hua Lin

    (Shanghai University)

  • Xide Zhu

    (Shanghai University)

Abstract

In this paper, we propose several new constraint qualifications for mathematical programs with second-order cone complementarity constraints (SOCMPCC), named SOCMPCC-K-, strongly (S-), and Mordukhovich (M-) relaxed constant positive linear dependence condition (K-/S-/M-RCPLD). We show that K-/S-/M-RCPLD can ensure that a local minimizer of SOCMPCC is a K-/S-/M-stationary point, respectively. We further give some other constant rank-type constraint qualifications for SOCMPCC. These new constraint qualifications are strictly weaker than SOCMPCC linear independent constraint qualification and nondegenerate condition. Finally, we demonstrate the relationships among the existing SOCMPCC constraint qualifications.

Suggested Citation

  • Yan-Chao Liang & Yue-Wen Liu & Gui-Hua Lin & Xide Zhu, 2023. "New Constraint Qualifications for Mathematical Programs with Second-Order Cone Complementarity Constraints," Journal of Optimization Theory and Applications, Springer, vol. 199(3), pages 1249-1280, December.
    • Handle: RePEc:spr:joptap:v:199:y:2023:i:3:d:10.1007_s10957-023-02299-w
    DOI: 10.1007/s10957-023-02299-w
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