Matrix analysis
A nonsmooth version of Newton's method
Mathematical Programming: Series A and B
Solution of monotone complementarity problems with locally Lipschitzian functions
Mathematical Programming: Series A and B - Special issue on computational nonsmooth optimization
Merit functions for semi-definite complementarity problems
Mathematical Programming: Series A and B
Smoothing Functions for Second-Order-Cone Complementarity Problems
SIAM Journal on Optimization
Semidefinite Programs: New Search Directions, Smoothing-Type Methods, and Numerical Results
SIAM Journal on Optimization
Regularity Properties of a Semismooth Reformulation of Variational Inequalities
SIAM Journal on Optimization
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
Constraint Nondegeneracy, Strong Regularity, and Nonsingularity in Semidefinite Programming
SIAM Journal on Optimization
Nonsingularity of FB system and constraint nondegeneracy in semidefinite programming
Numerical Algorithms
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For a locally optimal solution to the nonlinear semidefinite programming problem, under Robinson's constraint qualification, we show that the nonsingularity of Clarke's Jacobian of the Fischer-Burmeister (FB) nonsmooth system is equivalent to the strong regularity of the Karush-Kuhn-Tucker point. Consequently, from Sun's paper [Math. Oper. Res., 31 (2006), pp. 761-776] the semismooth Newton method applied to the FB system may attain the locally quadratic convergence under the strong second order sufficient condition and constraint nondegeneracy.