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.