We consider a Newton-type method for the solution of semidefinite programs. This Newton-type method is based on a semismooth reformulation of the semidefinite program as a nonsmooth system of equations. We establish local quadratic convergence of this method under a linear independence assumption and a slightly modified nondegeneracy condition. In contrast to previous investigations, however, the strict complementarity condition is not needed in our analysis.
The aim of this paper is now to have a closer look at the local convergence behaviour of a nonsmooth Newton-type method for the solution of the optimality conditions. It turns out that we can prove local quadratic convergence of this method under a linear independence condition and a certain nondegeneracy condition which is slightly different from a standard nondegeneracy condition used within the local analysis of some other methods for solving semidefinite programs. However, in contrast to these other methods, we do not need the strict complementarity condition.
Source: University of Wurzburg
Author: Christian Kanzow | Christian Nagel
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