Numerical study of a smoothing algorithm for the complementarity system over the second-order cone

Journal Article · Sun Jul 15 00:00:00 EDT 2018 · Computational and Applied Mathematics

DOI:https://doi.org/10.1007/S40314-017-0485-2· OSTI ID:22769291

Dong, Li; Tang, Jingyong; Song, Xinyu ^[1]

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1. Xinyang Normal University, School of Mathematics and Statistics (China)

This paper deals with the complementarity system over the second-order cone (denoted by CSSOC) which contains a wide class of problems. We extend a class of regularized Chen–Harker–Kanzow–Smale smoothing functions studied by Huang and Sun (Appl Math Optim 52:237–262, 2005) for the linear complementarity problem to the CSSOC. Based on this class of functions, we propose a smoothing algorithm for solving the CSSOC. Under weak assumptions, we prove that the proposed algorithm has global and local quadratic convergence. The proposed algorithm is different from existing smoothing algorithms for solving the CSSOC because it adopts a new nonmonotone line search rule. In addition, our algorithm solves a new equation reformulation of the CSSOC. Numerical experiments indicate that the proposed algorithm is quite effective.

• OSTI ID: 22769291
• Journal Information: Computational and Applied Mathematics, Vol. 37, Issue 3; Other Information: Copyright (c) 2018 SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional; Country of input: International Atomic Energy Agency (IAEA); ISSN 0101-8205
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICAL METHODS AND COMPUTING
ALGORITHMS
CONES
CONVERGENCE
EQUATIONS
FUNCTIONS
NUMERICAL ANALYSIS
SUN