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

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-R...

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Veröffentlicht in:Journal of optimization theory and applications Jg. 199; H. 3; S. 1249 - 1280
Hauptverfasser: Liang, Yan-Chao, Liu, Yue-Wen, Lin, Gui-Hua, Zhu, Xide
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York Springer US 01.12.2023
Springer Nature B.V
Schlagworte:
Algorithms
Applications of Mathematics
Approximation
Calculus of Variations and Optimal Control; Optimization
Constraints
Engineering
Information science
Mathematical analysis
Mathematical programming
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Qualifications
Theory of Computation
SOCMPCC nondegenerate condition
Constraint qualification
90C30
SOCMPCC relaxed constant positive linear dependence condition
90C33
Mathematical program with second-order cone complementarity constrains
ISSN:0022-3239, 1573-2878
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Zusammenfassung: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.
Bibliographie:ObjectType-Article-1
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ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-023-02299-w