A semidefinite relaxation method for second-order cone polynomial complementarity problems

This paper discusses how to compute all real solutions of the second-order cone tensor complementarity problem when there are finitely many ones. For this goal, we first formulate the second-order cone tensor complementarity problem as two polynomial optimization problems. Based on the reformulation...

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Veröffentlicht in:	Computational optimization and applications 2020-04, Vol.75 (3), p.629-647
Hauptverfasser:	Cheng, Lulu, Zhang, Xinzhen
Format:	Artikel
Sprache:	eng
Schlagworte:	Convex and Discrete Geometry Management Science Mathematics Mathematics and Statistics Operations Research Operations Research/Decision Theory Optimization Polynomials Relaxation method (mathematics) Statistics Tensors
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Zusammenfassung:	This paper discusses how to compute all real solutions of the second-order cone tensor complementarity problem when there are finitely many ones. For this goal, we first formulate the second-order cone tensor complementarity problem as two polynomial optimization problems. Based on the reformulation, a semidefinite relaxation method is proposed by solving a finite number of semidefinite relaxations with some assumptions. Numerical experiments are given to show the efficiency of the method.
ISSN:	0926-6003 1573-2894
DOI:	10.1007/s10589-019-00162-1