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

Yan-Chao Liang (), Yue-Wen Liu (), Gui-Hua Lin () and Xide Zhu ()
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Yan-Chao Liang: Henan Normal University
Yue-Wen Liu: Henan Normal University
Gui-Hua Lin: Shanghai University
Xide Zhu: Shanghai University

Journal of Optimization Theory and Applications, 2023, vol. 199, issue 3, No 15, 1249-1280

Abstract: 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.

Keywords: Mathematical program with second-order cone complementarity constrains; Constraint qualification; SOCMPCC nondegenerate condition; SOCMPCC relaxed constant positive linear dependence condition; 90C30; 90C33 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10957-023-02299-w

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