Open AccessSemidefinite relaxation method for polynomial optimization with second-order cone complementarity constraints
Author(s) -
Lin Zhu,
Xinzhen Zhang
Publication year - 2022
Publication title -
journal of industrial and management optimization
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.325
H-Index - 32
eISSN - 1553-166X
pISSN - 1547-5816
DOI - 10.3934/jimo.2021030
Subject(s) - complementarity (molecular biology) , relaxation (psychology) , mathematics , semidefinite programming , cone (formal languages) , polynomial , second order cone programming , complementarity theory , mathematical optimization , algorithm , mathematical analysis , convex optimization , geometry , physics , nonlinear system , psychology , social psychology , genetics , regular polygon , quantum mechanics , biology
Polynomial optimization problem with second-order cone complementarity constraints (SOCPOPCC) is a special case of mathematical program with second-order cone complementarity constraints (SOCMPCC). In this paper, we consider how to apply Lasserre's type of semidefinite relaxation method to solve SOCPOPCC. To this end, we first reformulate SOCPOPCC equivalently as a polynomial optimization and then solve the reformulated polynomial optimization with semidefinite relaxation method. For a special case of SOCPOPCC, we present another reformulation of polynomial optimization, which is of lower degree. SDP relaxation method is applied to solve the new polynomial optimization. Numerical examples are reported to show the efficiency of our proposed method.