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

被引：51

作者：

Chen, Jein-Shan ^{[1
]}

机构：

[1] Natl Taiwan Normal Univ, Dept Math, Taipei 11677, Taiwan

来源：

MATHEMATICAL METHODS OF OPERATIONS RESEARCH | 2006年 / 64卷 / 03期

关键词：

error bound; Jordan product; level set; merit function; second-order cone; spectral factorization;

D O I：

10.1007/s00186-006-0098-9

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

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.

引用

页码：495 / 519

页数：25

共 27 条

[1]

ALIZADEH F, 2000, HDB SEMIDEFINITE PRO, P195

[2] On implementing a primal-dual interior-point method for conic quadratic optimization [J].

Andersen, ED ;

Roos, C ;

Terlaky, T .

MATHEMATICAL PROGRAMMING, 2003, 95 (02) :249-277

[3] An unconstrained smooth minimization reformulation of the second-order cone complementarity problem [J].

Chen, JS ;

Tseng, P .

MATHEMATICAL PROGRAMMING, 2005, 104 (2-3) :293-327

[4] Analysis of nonsmooth vector-valued functions associated with second-order cones [J].

Chen, JS ;

Chen, X ;

Tseng, P .

MATHEMATICAL PROGRAMMING, 2004, 101 (01) :95-117

[5]

CHEN JS, 2006, PAC J OPTIM, V2, P167

[6] Complementarity functions and numerical experiments on some smoothing newton methods for second-order-cone complementarity problems [J].

Chen, XD ;

Sun, D ;

Sun, J .

COMPUTATIONAL OPTIMIZATION AND APPLICATIONS, 2003, 25 (1-3) :39-56

[7]

FACCHINEI F, 2003, FINITE DIMENSIONAL V, V1, DOI DOI 10.1007/978-0-387-21815-16

[8]

Facchinei Francisco., 2003, FINITE DIMENSIONAL V, V2

[9]

FARAUT U, 1994, OXFORD MATH MONOGRAP

[10] Solution of monotone complementarity problems with locally Lipschitzian functions [J].

Fischer, A .

MATHEMATICAL PROGRAMMING, 1997, 76 (03) :513-532

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