A matrix-splitting method for symmetric affine second-order cone complementarity problems
Journal of Computational and Applied Mathematics
A multisplitting method for symmetrical affine second-order cone complementarity problem
Computers & Mathematics with Applications
Box-constrained minimization reformulations of complementarity problems in second-order cones
Journal of Global Optimization
A smoothing-type algorithm for solving system of inequalities
Journal of Computational and Applied Mathematics
A one-step smoothing Newton method for second-order cone programming
Journal of Computational and Applied Mathematics
A smoothing method for second order cone complementarity problem
Journal of Computational and Applied Mathematics
Log-Sigmoid nonlinear Lagrange method for nonlinear optimization problems over second-order cones
Journal of Computational and Applied Mathematics
A nonmonotone smoothing Newton algorithm for solving nonlinear complementarity problems
Optimization Methods & Software
A matrix-splitting method for symmetric affine second-order cone complementarity problems
Journal of Computational and Applied Mathematics
Computational Optimization and Applications
A one-parametric class of merit functions for the second-order cone complementarity problem
Computational Optimization and Applications
Smoothing algorithms for complementarity problems over symmetric cones
Computational Optimization and Applications
Solvability of Newton equations in smoothing-type algorithms for the SOCCP
Journal of Computational and Applied Mathematics
Computers & Mathematics with Applications
SIAM Journal on Optimization
A Continuation Method for Nonlinear Complementarity Problems over Symmetric Cones
SIAM Journal on Optimization
A class of nonlinear Lagrangians for nonconvex second order cone programming
Computational Optimization and Applications
The penalized Fischer-Burmeister SOC complementarity function
Computational Optimization and Applications
Journal of Global Optimization
A proximal point algorithm for the monotone second-order cone complementarity problem
Computational Optimization and Applications
The solution set structure of monotone linear complementarity problems over second-order cone
Operations Research Letters
Journal of Global Optimization
Information Sciences: an International Journal
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The second-order cone complementarity problem (SOCCP) is a wide class of problems containing the nonlinear complementarity problem (NCP) and the second-order cone programming problem (SOCP). Recently, Fukushima, Luo, and Tseng [SIAM J. Optim., 12 (2001), pp. 436--460] extended some merit functions and their smoothing functions for NCP to SOCCP. Moreover, they derived computable formulas for the Jacobians of the smoothing functions and gave conditions for the Jacobians to be invertible. In this paper, we propose a globally and quadratically convergent algorithm, which is based on smoothing and regularization methods, for solving monotone SOCCP. In particular, we study strong semismoothness and Jacobian consistency, which play an important role in establishing quadratic convergence of the algorithm. Furthermore, we examine the effectiveness of the algorithm by means of numerical experiments.