Quadratic Convergence of a Squared Smoothing Newton Method for Nonsmooth Matrix Equations and Its Applications in Semidefinite Optimization Problems

We study a smoothing Newton method for solving a nonsmooth matrix equation that includes semidefinite programming and the semidefinte 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. We also establish quadratic convergence of this … Read more