A descent method for a reformulation of the second-order cone complementarity problem
Journal of Computational and Applied Mathematics
A smoothing method for second order cone complementarity problem
Journal of Computational and Applied Mathematics
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
A Continuation Method for Nonlinear Complementarity Problems over Symmetric Cones
SIAM Journal on Optimization
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
Neural networks for solving second-order cone constrained variational inequality problem
Computational Optimization and Applications
Stationary point conditions for the FB merit function associated with symmetric cones
Operations Research Letters
The SC1 property of the squared norm of the SOC Fischer-Burmeister function
Operations Research Letters
The solution set structure of monotone linear complementarity problems over second-order cone
Operations Research Letters
An alternating direction method for second-order conic programming
Computers and Operations Research
Information Sciences: an International Journal
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A popular approach to solving the nonlinear complementarity problem (NCP) is to reformulate it as the global minimization of a certain merit function over ℝn. A popular choice of the merit function is the squared norm of the Fischer-Burmeister function, shown to be smooth over ℝn and, for monotone NCP, each stationary point is a solution of the NCP. This merit function and its analysis were subsequently extended to the semidefinite complementarity problem (SDCP), although only differentiability, not continuous differentiability, was established. In this paper, we extend this merit function and its analysis, including continuous differentiability, to the second-order cone complementarity problem (SOCCP). Although SOCCP is reducible to a SDCP, the reduction does not allow for easy translation of the analysis from SDCP to SOCCP. Instead, our analysis exploits properties of the Jordan product and spectral factorization associated with the second-order cone. We also report preliminary numerical experience with solving DIMACS second-order cone programs using a limited-memory BFGS method to minimize the merit function.