A smoothing Newton method for a type of inverse semi-definite quadratic programming problem
Journal of Computational and Applied Mathematics
Smoothing algorithms for complementarity problems over symmetric cones
Computational Optimization and Applications
Computers & Mathematics with Applications
A Continuation Method for Nonlinear Complementarity Problems over Symmetric Cones
SIAM Journal on Optimization
A proximal point algorithm for the monotone second-order cone complementarity problem
Computational Optimization and Applications
Nonsingularity Conditions for the Fischer-Burmeister System of Nonlinear SDPs
SIAM Journal on Optimization
Nonsingularity of FB system and constraint nondegeneracy in semidefinite programming
Numerical Algorithms
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We study a smoothing Newton method for solving a nonsmooth matrix equation that includes semidefinite programming and the semidefinite complementarity problem as special cases. This method, if specialized for solving semidefinite programs, needs to solve only one linear system per iteration and achieves quadratic convergence under strict complementarity and nondegeneracy. We also establish quadratic convergence of this method applied to the semidefinite complementarity problem under the assumption that the Jacobian of the problem is positive definite on the affine hull of the critical cone at the solution. These results are based on the strong semismoothness and complete characterization of the B-subdifferential of a corresponding squared smoothing matrix function, which are of general theoretical interest.