A descent method for a reformulation of the second-order cone complementarity problem

Jein Shan Chen, Shaohua Pan

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

Analogous to the nonlinear complementarity problem and the semi-definite complementarity problem, a popular approach to solving the second-order cone complementarity problem (SOCCP) is to reformulate it as an unconstrained minimization of a certain merit function over Rn. In this paper, we present a descent method for solving the unconstrained minimization reformulation of the SOCCP which is based on the Fischer-Burmeister merit function (FBMF) associated with second-order cone [J.-S. Chen, P. Tseng, An unconstrained smooth minimization reformulation of the second-order cone complementarity problem, Math. Programming 104 (2005) 293-327], and prove its global convergence. Particularly, we compare the numerical performance of the method for the symmetric affine SOCCP generated randomly with the FBMF approach [J.-S. Chen, P. Tseng, An unconstrained smooth minimization reformulation of the second-order cone complementarity problem, Math. Programming 104 (2005) 293-327]. The comparison results indicate that, if a scaling strategy is imposed on the test problem, the descent method proposed is comparable with the merit function approach in the CPU time for solving test problems although the former may require more function evaluations.

Original languageEnglish
Pages (from-to)547-558
Number of pages12
JournalJournal of Computational and Applied Mathematics
Volume213
Issue number2
DOIs
Publication statusPublished - 2008 Apr 1

Fingerprint

Second-order Cone
Descent Method
Complementarity Problem
Reformulation
Cones
Merit Function
Unconstrained Minimization
Test Problems
Programming
Nonlinear Complementarity Problem
Function evaluation
Comparison Result
Evaluation Function
CPU Time
Global Convergence
Program processors
Scaling

Keywords

  • Complementarity
  • Descent method
  • Merit function
  • Second-order cone

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

Cite this

A descent method for a reformulation of the second-order cone complementarity problem. / Chen, Jein Shan; Pan, Shaohua.

In: Journal of Computational and Applied Mathematics, Vol. 213, No. 2, 01.04.2008, p. 547-558.

Research output: Contribution to journalArticle

@article{d7eb2e19c5ee4ba2b3e5168a8843cb30,
title = "A descent method for a reformulation of the second-order cone complementarity problem",
abstract = "Analogous to the nonlinear complementarity problem and the semi-definite complementarity problem, a popular approach to solving the second-order cone complementarity problem (SOCCP) is to reformulate it as an unconstrained minimization of a certain merit function over Rn. In this paper, we present a descent method for solving the unconstrained minimization reformulation of the SOCCP which is based on the Fischer-Burmeister merit function (FBMF) associated with second-order cone [J.-S. Chen, P. Tseng, An unconstrained smooth minimization reformulation of the second-order cone complementarity problem, Math. Programming 104 (2005) 293-327], and prove its global convergence. Particularly, we compare the numerical performance of the method for the symmetric affine SOCCP generated randomly with the FBMF approach [J.-S. Chen, P. Tseng, An unconstrained smooth minimization reformulation of the second-order cone complementarity problem, Math. Programming 104 (2005) 293-327]. The comparison results indicate that, if a scaling strategy is imposed on the test problem, the descent method proposed is comparable with the merit function approach in the CPU time for solving test problems although the former may require more function evaluations.",
keywords = "Complementarity, Descent method, Merit function, Second-order cone",
author = "Chen, {Jein Shan} and Shaohua Pan",
year = "2008",
month = "4",
day = "1",
doi = "10.1016/j.cam.2007.01.029",
language = "English",
volume = "213",
pages = "547--558",
journal = "Journal of Computational and Applied Mathematics",
issn = "0377-0427",
publisher = "Elsevier",
number = "2",

}

TY - JOUR

T1 - A descent method for a reformulation of the second-order cone complementarity problem

AU - Chen, Jein Shan

AU - Pan, Shaohua

PY - 2008/4/1

Y1 - 2008/4/1

N2 - Analogous to the nonlinear complementarity problem and the semi-definite complementarity problem, a popular approach to solving the second-order cone complementarity problem (SOCCP) is to reformulate it as an unconstrained minimization of a certain merit function over Rn. In this paper, we present a descent method for solving the unconstrained minimization reformulation of the SOCCP which is based on the Fischer-Burmeister merit function (FBMF) associated with second-order cone [J.-S. Chen, P. Tseng, An unconstrained smooth minimization reformulation of the second-order cone complementarity problem, Math. Programming 104 (2005) 293-327], and prove its global convergence. Particularly, we compare the numerical performance of the method for the symmetric affine SOCCP generated randomly with the FBMF approach [J.-S. Chen, P. Tseng, An unconstrained smooth minimization reformulation of the second-order cone complementarity problem, Math. Programming 104 (2005) 293-327]. The comparison results indicate that, if a scaling strategy is imposed on the test problem, the descent method proposed is comparable with the merit function approach in the CPU time for solving test problems although the former may require more function evaluations.

AB - Analogous to the nonlinear complementarity problem and the semi-definite complementarity problem, a popular approach to solving the second-order cone complementarity problem (SOCCP) is to reformulate it as an unconstrained minimization of a certain merit function over Rn. In this paper, we present a descent method for solving the unconstrained minimization reformulation of the SOCCP which is based on the Fischer-Burmeister merit function (FBMF) associated with second-order cone [J.-S. Chen, P. Tseng, An unconstrained smooth minimization reformulation of the second-order cone complementarity problem, Math. Programming 104 (2005) 293-327], and prove its global convergence. Particularly, we compare the numerical performance of the method for the symmetric affine SOCCP generated randomly with the FBMF approach [J.-S. Chen, P. Tseng, An unconstrained smooth minimization reformulation of the second-order cone complementarity problem, Math. Programming 104 (2005) 293-327]. The comparison results indicate that, if a scaling strategy is imposed on the test problem, the descent method proposed is comparable with the merit function approach in the CPU time for solving test problems although the former may require more function evaluations.

KW - Complementarity

KW - Descent method

KW - Merit function

KW - Second-order cone

UR - http://www.scopus.com/inward/record.url?scp=38549168534&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=38549168534&partnerID=8YFLogxK

U2 - 10.1016/j.cam.2007.01.029

DO - 10.1016/j.cam.2007.01.029

M3 - Article

AN - SCOPUS:38549168534

VL - 213

SP - 547

EP - 558

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

SN - 0377-0427

IS - 2

ER -