On the generalized Fischer-Burmeister merit function for the second-order cone complementarity problem

Shaohua Pan; Sangho Kum; Yongdo Lim; Jein Shan Chen

doi:10.1090/S0025-5718-2013-02742-1

On the generalized Fischer-Burmeister merit function for the second-order cone complementarity problem

Shaohua Pan, Sangho Kum, Yongdo Lim, Jein Shan Chen

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

13 Citations (Scopus)

Abstract

It has been an open question whether the family of merit functions φ_p (p > 1), the generalized Fischer-Burmeister (FB) merit function, associated to the second-order cone is smooth or not. In this paper we answer it partly, and show that φ_p is smooth for p ∈ (1, 4), and we provide the condition for its coerciveness. Numerical results are reported to illustrate the influence of p on the performance of the merit function method based on φ_p.

Original language	English
Pages (from-to)	1143-1171
Number of pages	29
Journal	Mathematics of Computation
Volume	83
Issue number	287
DOIs	https://doi.org/10.1090/S0025-5718-2013-02742-1
Publication status	Published - 2014 May

Keywords

Complementarity problem
Generalized FB merit function
Second-order cones

ASJC Scopus subject areas

Algebra and Number Theory
Computational Mathematics
Applied Mathematics

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10.1090/S0025-5718-2013-02742-1

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abstract = "It has been an open question whether the family of merit functions φp (p > 1), the generalized Fischer-Burmeister (FB) merit function, associated to the second-order cone is smooth or not. In this paper we answer it partly, and show that φp is smooth for p ∈ (1, 4), and we provide the condition for its coerciveness. Numerical results are reported to illustrate the influence of p on the performance of the merit function method based on φp.",

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AB - It has been an open question whether the family of merit functions φp (p > 1), the generalized Fischer-Burmeister (FB) merit function, associated to the second-order cone is smooth or not. In this paper we answer it partly, and show that φp is smooth for p ∈ (1, 4), and we provide the condition for its coerciveness. Numerical results are reported to illustrate the influence of p on the performance of the merit function method based on φp.

KW - Complementarity problem

KW - Generalized FB merit function

KW - Second-order cones

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JO - Mathematics of Computation

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On the generalized Fischer-Burmeister merit function for the second-order cone complementarity problem

Abstract

Keywords

ASJC Scopus subject areas

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