A nonsmooth version of Newton's method
Mathematical Programming: Series A and B
Convergence analysis of some algorithms for solving nonsmooth equations
Mathematics of Operations Research
Some Noninterior Continuation Methods for LinearComplementarity Problems
SIAM Journal on Matrix Analysis and Applications
Smoothing Functions for Second-Order-Cone Complementarity Problems
SIAM Journal on Optimization
Computational Optimization and Applications
SIAM Journal on Optimization
A note on treating a second order cone program as a special case of a semidefinite program
Mathematical Programming: Series A and B
Strong Semismoothness of the Fischer-Burmeister SDC and SOC Complementarity Functions
Mathematical Programming: Series A and B
An unconstrained smooth minimization reformulation of the second-order cone complementarity problem
Mathematical Programming: Series A and B
Smoothing algorithms for complementarity problems over symmetric cones
Computational Optimization and Applications
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In this paper, we propose a globally and quadratically convergent Newton-type algorithm for solving monotone second-order cone complementarity problems (denoted by SOCCPs). This algorithm is based on smoothing and regularization techniques by incorporating smoothing Newton's method. Many Newton-type methods with smoothing and regularization techniques have been studied for solving nonlinear complementarity problems (NCPs) and box constrained variational inequalities (BVIs). Our algorithm is regarded as an extension of those methods to SOCCP. However, it is different from the existing methods, because we solve SOCCP by treating both the smoothing parameter @m and the regularization parameter @e as independent variables. In addition, numerical experiments indicate that the proposed method is quite effective.