Matrix analysis
A nonmonotone line search technique for Newton's method
SIAM Journal on Numerical Analysis
A nonsmooth version of Newton's method
Mathematical Programming: Series A and B
SIAM Review
Local convergence of predictor-corrector infeasible-interior-point algorithms for SDPs and SDLCPs
Mathematical Programming: Series A and B
Merit functions for semi-definite complementarity problems
Mathematical Programming: Series A and B
SIAM Journal on Optimization
Semismooth Matrix-Valued Functions
Mathematics of Operations Research
Semismooth homeomorphisms and strong stability of semidefinite and Lorentz complementarity problems
Mathematics of Operations Research
SIAM Journal on Optimization
SIAM Journal on Optimization
Strong Semismoothness of the Fischer-Burmeister SDC and SOC Complementarity Functions
Mathematical Programming: Series A and B
Mathematics of Operations Research
The rate of convergence of the augmented Lagrangian method for nonlinear semidefinite programming
Mathematical Programming: Series A and B
Constraint Nondegeneracy, Strong Regularity, and Nonsingularity in Semidefinite Programming
SIAM Journal on Optimization
Regularization Methods for Semidefinite Programming
SIAM Journal on Optimization
A Newton-CG Augmented Lagrangian Method for Semidefinite Programming
SIAM Journal on Optimization
Nonsingularity Conditions for the Fischer-Burmeister System of Nonlinear SDPs
SIAM Journal on Optimization
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For a KKT point of the linear semidefinite programming (SDP), we show that the nonsingularity of the B-subdifferential of Fischer-Burmeister (FB) nonsmooth system, the nonsingularity of Clarke's Jacobian of this system, and the primal and dual constraint nondegeneracies, are all equivalent. Also, each of these conditions is equivalent to the nonsingularity of Clarke's Jacobian of the smoothed counterpart of FB nonsmooth system, which particularly implies that the FB smoothing Newton method may attain the local quadratic convergence without strict complementarity assumption. We also report numerical results of the FB smoothing method for some benchmark problems.