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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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    References listed on IDEAS

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    1. Lei Guo & Gui-Hua Lin, 2013. "Notes on Some Constraint Qualifications for Mathematical Programs with Equilibrium Constraints," Journal of Optimization Theory and Applications, Springer, vol. 156(3), pages 600-616, March.
    2. Roberto Andreani & Gabriel Haeser & Leonardo M. Mito & C. Héctor Ramírez & Thiago P. Silveira, 2022. "Global Convergence of Algorithms Under Constant Rank Conditions for Nonlinear Second-Order Cone Programming," Journal of Optimization Theory and Applications, Springer, vol. 195(1), pages 42-78, October.
    3. X. M. Hu & D. Ralph, 2004. "Convergence of a Penalty Method for Mathematical Programming with Complementarity Constraints," Journal of Optimization Theory and Applications, Springer, vol. 123(2), pages 365-390, November.
    4. Lei Guo & Zhibin Deng, 2022. "A New Augmented Lagrangian Method for MPCCs—Theoretical and Numerical Comparison with Existing Augmented Lagrangian Methods," Mathematics of Operations Research, INFORMS, vol. 47(2), pages 1229-1246, May.
    5. Holger Scheel & Stefan Scholtes, 2000. "Mathematical Programs with Complementarity Constraints: Stationarity, Optimality, and Sensitivity," Mathematics of Operations Research, INFORMS, vol. 25(1), pages 1-22, February.
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    7. Xide Zhu & Jin Zhang & Jinchuan Zhou & Xinmin Yang, 2019. "Mathematical Programs with Second-Order Cone Complementarity Constraints: Strong Stationarity and Approximation Method," Journal of Optimization Theory and Applications, Springer, vol. 181(2), pages 521-540, May.
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