Department of Applied Mathematics & Physics, Kyoto Univiversity

Technical Report #98012 (July, 1998)

A Nonsmooth Equation Based BFGS Method for Solving KKT Systems in Mathematical Programming
by Donghui Li, Nobuo Yamashita and Masao Fukushima

In this paper, we present a BFGS method for solving a KKT system in mathematical programming, based on a nonsmooth equation reformulation of the KKT system. We successively split the nonsmooth equation into equivalent equations with particular structure. Based on the splitting, we develop a BFGS method in which subproblems are systems of linear equations with symmetric and positive definite coefficient matrices. A suitable line search is introduced under which the generated iterates exhibit an approximately norm decent property. The method is well defined and, under suitable conditions, converges to a KKT point globally and superlinearly without convexity assumption on the problem.