Linear complementarity problems on extended second order cones

2017/07/13 by S. Z. Németh, Lianghai Xiao, L. Xiao +2
Computer Science · Mathematics · #Advanced Optimization Algorithms Research #Applied mathematics #Complementarity (molecular biology) #Complementarity theory #Computer science #FOS: Mathematics #First order #Linear complementarity problem #Mathematical optimization #Mathematics #Matrix Theory and Algorithms #Mixed complementarity problem #Nonlinear system #Optimization and Control (math.OC) #Optimization and Variational Analysis #Orthant #Physics #math.OC

paper · pdf · doi:10.48550/arxiv.1707.04268

openalex publication_date 2017/07/13 · arxiv created 2018/01/19 · arxiv updated 2018/01/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

In this paper, we study the linear complementarity problems on extended second order cones. We convert a linear complementarity problem on an extended second order cone into a mixed complementarity problem on the non-negative orthant. We state necessary and sufficient conditions for a point to be a solution of the converted problem. We also present solution strategies for this problem, such as the Newton method and Levenberg-Marquardt algorithm. Finally, we present some numerical examples.

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