TY - JOUR

T1 - A damped Gauss-Newton method for the second-order cone complementarity problem

AU - Pan, Shaohua

AU - Chen, Jein Shan

N1 - Funding Information:
S. Pan’s work is partially supported by the Doctoral Starting-up Foundation (B13B6050640) of GuangDong Province.
Funding Information:
J.-S. Chen is member of Mathematics Division, National Center for Theoretical Sciences, Taipei Office. J.-S. Chen’s work is partially supported by National Science Council of Taiwan.

PY - 2009/6

Y1 - 2009/6

N2 - We investigate some properties related to the generalized Newton method for the Fischer-Burmeister (FB) function over second-order cones, which allows us to reformulate the second-order cone complementarity problem (SOCCP) as a semismooth system of equations. Specifically, we characterize the B-subdifferential of the FB function at a general point and study the condition for every element of the B-subdifferential at a solution being nonsingular. In addition, for the induced FB merit function, we establish its coerciveness and provide a weaker condition than Chen and Tseng (Math. Program. 104:293-327, 2005) for each stationary point to be a solution, under suitable Cartesian P-properties of the involved mapping. By this, a damped Gauss-Newton method is proposed, and the global and superlinear convergence results are obtained. Numerical results are reported for the second-order cone programs from the DIMACS library, which verify the good theoretical properties of the method.

AB - We investigate some properties related to the generalized Newton method for the Fischer-Burmeister (FB) function over second-order cones, which allows us to reformulate the second-order cone complementarity problem (SOCCP) as a semismooth system of equations. Specifically, we characterize the B-subdifferential of the FB function at a general point and study the condition for every element of the B-subdifferential at a solution being nonsingular. In addition, for the induced FB merit function, we establish its coerciveness and provide a weaker condition than Chen and Tseng (Math. Program. 104:293-327, 2005) for each stationary point to be a solution, under suitable Cartesian P-properties of the involved mapping. By this, a damped Gauss-Newton method is proposed, and the global and superlinear convergence results are obtained. Numerical results are reported for the second-order cone programs from the DIMACS library, which verify the good theoretical properties of the method.

KW - B-subdifferential

KW - Complementarity

KW - Fischer-Burmeister function

KW - Generalized Newton method

KW - Second-order cones

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U2 - 10.1007/s00245-008-9054-9

DO - 10.1007/s00245-008-9054-9

M3 - Article

AN - SCOPUS:63049104088

SN - 0095-4616

VL - 59

SP - 293

EP - 318

JO - Applied Mathematics and Optimization

JF - Applied Mathematics and Optimization

IS - 3

ER -