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Journal of Applied Mathematics and Computing

Erschienen in:

01.10.2013 | Original Research

The convergence of a modified smoothing-type algorithm for the symmetric cone complementarity problem

verfasst von: Jingyong Tang, Li Dong, Liang Fang, Jinchuan Zhou

Erschienen in: Journal of Applied Mathematics and Computing | Ausgabe 1-2/2013

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Abstract

The symmetric cone complementarity problem (denoted by SCCP) is a broad class of optimization problems, which contains the semidefinite complementarity problem, the second-order cone complementarity problem, and the nonlinear complementarity problem. In this paper we first extend the smoothing function proposed by Huang et al. (Sci. China 44:1107–1114, 2001) for the nonlinear complementarity problem to the context of symmetric cones and show that it is coercive under suitable assumptions. Based on this smoothing function, a smoothing-type algorithm, which is a modified version of the Qi-Sun-Zhou method (Qi et al. in Math. Program. 87:1–35, 2000), is proposed for solving the SCCP. By using the theory of Euclidean Jordan algebras, we prove that the proposed algorithm is globally and locally quadratically convergent under suitable assumptions. Preliminary numerical results for some second-order cone complementarity problems are reported which indicate that the proposed algorithm is effective.

Vorheriger Artikel Existence and uniqueness results for Cauchy problem of variable-order fractional differential equations

Nächster Artikel The threshold between permanence and extinction for a stochastic Logistic model with regime switching

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Titel: The convergence of a modified smoothing-type algorithm for the symmetric cone complementarity problem
verfasst von: Jingyong Tang
Li Dong
Liang Fang
Jinchuan Zhou
Publikationsdatum: 01.10.2013
Verlag: Springer Berlin Heidelberg
Erschienen in: Journal of Applied Mathematics and Computing / Ausgabe 1-2/2013
Print ISSN: 1598-5865
Elektronische ISSN: 1865-2085
DOI: https://doi.org/10.1007/s12190-013-0665-1

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