A continuation method for (strongly) monotone variational inequalities
Mathematical Programming: Series A and B
Smoothing Functions for Second-Order-Cone Complementarity Problems
SIAM Journal on Optimization
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
SIAM Journal on Optimization
An unconstrained smooth minimization reformulation of the second-order cone complementarity problem
Mathematical Programming: Series A and B
Cartesian P-property and Its Applications to the Semidefinite Linear Complementarity Problem
Mathematical Programming: Series A and B
A smoothing-type algorithm for solving system of inequalities
Journal of Computational and Applied Mathematics
A smoothing method for second order cone complementarity problem
Journal of Computational and Applied Mathematics
A regularized smoothing-type algorithm for solving a system of inequalities with a P0-function
Journal of Computational and Applied Mathematics
A nonmonotone smoothing-type algorithm for solving a system of equalities and inequalities
Journal of Computational and Applied Mathematics
| Hi-index | 7.29 |
In this paper, we first investigate the invertibility of a class of matrices. Based on the obtained results, we then discuss the solvability of Newton equations appearing in the smoothing-type algorithm for solving the second-order cone complementarity problem (SOCCP). A condition ensuring the solvability of such a system of Newton equations is given. In addition, our results also show that the assumption that the Jacobian matrix of the function involved in the SOCCP is a P"0-matrix is not enough for ensuring the solvability of such a system of Newton equations, which is different from the one of smoothing-type algorithms for solving many traditional optimization problems in @?^n.