Semismooth Reformulation and Nonsmooth Newton's Method for Solving Nonlinear Semidefinite Programming

摘要

In this paper, our interest is to solve canonical nonlinear semidefinite programming (NLSDP). First, we give a reformulation of the (KKT) system associated to the NLSDP as a nonsmooth equation by using the Fischer-Burmeister (FB) function. The nonsmooth equation is then solved by the nonsmooth Newton's method using formulas of the generalized Jacobian of the FB function given by L. Zhang et al. in [14]. Under mild conditions, we prove that the convergence is locally quadratic.