Two classes of merit functions for the second-order cone complementarity problem

Jein Shan Chen

doi:10.1007/s00186-006-0098-9

Two classes of merit functions for the second-order cone complementarity problem

Jein Shan Chen^*

^*Corresponding author for this work

Department of Mathematics

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

48 Citations (Scopus)

Abstract

Recently Tseng (Math Program 83:159-185, 1998) extended a class of merit functions, proposed by Luo and Tseng (A new class of merit functions for the nonlinear complementarity problem, in Complementarity and Variational Problems: State of the Art, pp. 204-225, 1997), for the nonlinear complementarity problem (NCP) to the semidefinite complementarity problem (SDCP) and showed several related properties. In this paper, we extend this class of merit functions to the second-order cone complementarity problem (SOCCP) and show analogous properties as in NCP and SDCP cases. In addition, we study another class of merit functions which are based on a slight modification of the aforementioned class of merit functions. Both classes of merit functions provide an error bound for the SOCCP and have bounded level sets.

Original language	English
Pages (from-to)	495-519
Number of pages	25
Journal	Mathematical Methods of Operations Research
Volume	64
Issue number	3
DOIs	https://doi.org/10.1007/s00186-006-0098-9
Publication status	Published - 2006 Dec

Keywords

Error bound
Jordan product
Level set
Merit function
Second-order cone
Spectral factorization

ASJC Scopus subject areas

Software
General Mathematics
Management Science and Operations Research

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10.1007/s00186-006-0098-9

Cite this

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abstract = "Recently Tseng (Math Program 83:159-185, 1998) extended a class of merit functions, proposed by Luo and Tseng (A new class of merit functions for the nonlinear complementarity problem, in Complementarity and Variational Problems: State of the Art, pp. 204-225, 1997), for the nonlinear complementarity problem (NCP) to the semidefinite complementarity problem (SDCP) and showed several related properties. In this paper, we extend this class of merit functions to the second-order cone complementarity problem (SOCCP) and show analogous properties as in NCP and SDCP cases. In addition, we study another class of merit functions which are based on a slight modification of the aforementioned class of merit functions. Both classes of merit functions provide an error bound for the SOCCP and have bounded level sets.",

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KW - Jordan product

KW - Level set

KW - Merit function

KW - Second-order cone

KW - Spectral factorization

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Two classes of merit functions for the second-order cone complementarity problem

Abstract

Keywords

ASJC Scopus subject areas

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