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

Lulu Cheng () and Xinzhen Zhang ()
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Lulu Cheng: Tianjin University
Xinzhen Zhang: Tianjin University

Computational Optimization and Applications, 2020, vol. 75, issue 3, No 3, 629-647

Abstract: Abstract 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.

Keywords: Tensor complementarity problem; Second-order cone; Lasserre’s hierarchy; Semidefinite relaxation; 15A18; 15A69; 90C22 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s10589-019-00162-1

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