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 -