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

Juhe Sun (), Bin Wang (), Li Wang (), Yanhong Yuan () and Yining Sun ()
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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

Mathematical Methods of Operations Research, 2025, vol. 101, issue 3, No 3, 435-458

Abstract: 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.

Keywords: Second-order cone double constrained variational inequality; Optimality condition; Stability analysis; Karush-Kuhn-Tucker (KKT) mapping (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s00186-025-00893-4

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