A nonmonotone line search technique for Newton's method
SIAM Journal on Numerical Analysis
Practical methods of optimization; (2nd ed.)
Practical methods of optimization; (2nd ed.)
A limited memory algorithm for bound constrained optimization
SIAM Journal on Scientific Computing
On the resolution of monotone complementarity problems
Computational Optimization and Applications
Nonlinear complementarity as unconstrained optimization
Journal of Optimization Theory and Applications
Solution of monotone complementarity problems with locally Lipschitzian functions
Mathematical Programming: Series A and B - Special issue on computational nonsmooth optimization
Associative and Jordan Algebras, and Polynomial Time Interior-Point Algorithms for Symmetric Cones
Mathematics of Operations Research
Smoothing Functions for Second-Order-Cone Complementarity Problems
SIAM Journal on Optimization
A New Merit Function For Nonlinear Complementarity Problems And A Related Algorithm
SIAM Journal on Optimization
Computational Optimization and Applications
An unconstrained smooth minimization reformulation of the second-order cone complementarity problem
Mathematical Programming: Series A and B
Complementarity: Applications, Algorithms and Extensions (Applied Optimization)
Complementarity: Applications, Algorithms and Extensions (Applied Optimization)
A smoothing method for second order cone complementarity problem
Journal of Computational and Applied Mathematics
Computational Optimization and Applications
A generalized Newton method for absolute value equations associated with second order cones
Journal of Computational and Applied Mathematics
Hi-index | 7.29 |
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 R^n. 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.