An Efficient Numerical Method for the Symmetric Positive Definite Second-Order Cone Linear Complementarity Problem

  • Xiang Wang
  • Xing Li
  • Lei-Hong Zhang
  • Ren-Cang LiEmail author


An efficient numerical method for solving a symmetric positive definite second-order cone linear complementarity problem (SOCLCP) is proposed. The method is shown to be more efficient than recently developed iterative methods for small-to-medium sized and dense SOCLCP. Therefore it can serve as an excellent core computational engine in solutions of large scale symmetric positive definite SOCLCP solved by subspace projection methods, solutions of general SOCLCP and the quadratic programming over a Cartesian product of multiple second-order cones, in which small-to-medium sized SOCLCPs have to be solved repeatedly, efficiently, and robustly.


Second-order cone Linear complementarity problem SOCLCP Globally uniquely solvable property GUS 

Mathematics Subject Classification

90C33 65K05 65F99 65F15 65F30 65P99 



The authors are grateful to two anonymous referees for their helpful comments and suggestions that improve the presentation. Wang is supported in part by the National Natural Science Foundation of China: NSFC-11461046, NSF of Jiangxi Province: 20161ACB21005 and 20181ACB20001, Zhang is supported in part by the National Natural Science Foundation of China: NSFC-11671246 and NSFC-91730303, and R.-C. Li is supported in part by NSF Grants: CCF-1527104 and DMS-1719620.


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Authors and Affiliations

  1. 1.Department of MathematicsNanchang UniversityNanchangChina
  2. 2.School of MathematicsShanghai University of Finance and EconomicsShanghaiChina
  3. 3.School of Mathematical SciencesSoochow UniversitySuzhouChina
  4. 4.Department of MathematicsUniversity of Texas at ArlingtonArlingtonUSA

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