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The Optimality Conditions and Stability Analysis for the Second-Order Cone Double Constrained Variational Inequalities

Author

Listed:
  • Juhe Sun

    (Shenyang Aerospace University)

  • Bin Wang

    (SINOPEC Shengli Oilfield Company)

  • Li Wang

    (Shenyang Aerospace University)

  • Yanhong Yuan

    (Taiyuan University of Technology)

  • Yining Sun

    (Shenyang Aerospace University)

Abstract

We provide the second-order cone double constrained variational inequalities (SOCDCVI) problem, which can be reduced to be the second-order cone coupled constrained variational inequalities problem. In order to provide the theoretical analysis for the convergence of algorithms to solve the corresponding second-order cone double variational inequalities problem, we firstly establish optimality conditions, including the first-order necessary and the second-order sufficient conditions. For the second-order cone double constrained variational inequality, we prove the first-order necessary conditions under Robinson constraint qualification, and the second-order sufficient conditions when the constraint sets satisfy outer seconder-order regularity condition. Secondly, by characterizing the generalized equation, the equivalence between the strongly regular solution and the Lipschitz homeomorphisms of the Karush-Kuhn-Tucker (KKT) mapping can be derived. With the strong second-order sufficient conditions under the constraints nondegeneracy conditions, we prove the nonsingularity of the Clarke’s generalized Jacobian of the KKT mapping. In addition, we introduce the uniform second-order growth conditions and the strong stability of local optimal solutions of the corresponding second-order cone double constrained optimization problem. Thus, by demonstrating several equivalent conclusions, we obtain the main stability theorem. The research results for the SOCDCVI problem will be a supplement for the study of variational inequalities.

Suggested Citation

  • Juhe Sun & Bin Wang & Li Wang & Yanhong Yuan & Yining Sun, 2025. "The Optimality Conditions and Stability Analysis for the Second-Order Cone Double Constrained Variational Inequalities," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 101(3), pages 435-458, June.
    • Handle: RePEc:spr:mathme:v:101:y:2025:i:3:d:10.1007_s00186-025-00893-4
    DOI: 10.1007/s00186-025-00893-4
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    References listed on IDEAS

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    1. Stephen M. Robinson, 1980. "Strongly Regular Generalized Equations," Mathematics of Operations Research, INFORMS, vol. 5(1), pages 43-62, February.
    2. Stephen M. Robinson, 2003. "Constraint Nondegeneracy in Variational Analysis," Mathematics of Operations Research, INFORMS, vol. 28(2), pages 201-232, May.
    3. Stephen M. Robinson, 1991. "An Implicit-Function Theorem for a Class of Nonsmooth Functions," Mathematics of Operations Research, INFORMS, vol. 16(2), pages 292-309, May.
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