A nonsmooth version of Newton's method
Mathematical Programming: Series A and B
Smoothing Functions for Second-Order-Cone Complementarity Problems
SIAM Journal on Optimization
Computational Optimization and Applications
Sub-quadratic convergence of a smoothing Newton algorithm for the P0– and monotone LCP
Mathematical Programming: Series A and B
Strong Semismoothness of the Fischer-Burmeister SDC and SOC Complementarity Functions
Mathematical Programming: Series A and B
Computational Optimization and Applications
A descent method for a reformulation of the second-order cone complementarity problem
Journal of Computational and Applied Mathematics
On equivalent reformulations for absolute value equations
Computational Optimization and Applications
Smoothing algorithms for complementarity problems over symmetric cones
Computational Optimization and Applications
A globally and quadratically convergent method for absolute value equations
Computational Optimization and Applications
Equilibrium problems involving the Lorentz cone
Journal of Global Optimization
| Hi-index | 7.30 |
In this paper, we introduce the absolute value equations associated with second order cones (SOCAVE in short), which is a generalization of the absolute value equations discussed recently in the literature. It is proved that the SOCAVE is equivalent to a class of second order cone linear complementarity problems (SOCLCP in short). In particular, we propose a generalized Newton method for solving the SOCAVE and show that the proposed method is globally linearly and locally quadratically convergent under suitable assumptions. We also report some preliminary numerical results of the proposed method for solving the SOCAVE and the SOCLCP, which show the efficiency of the proposed method.