Nonsmooth Equation Based BFGS Method for Solving KKT Systems in Mathematical Programming

D. H. Li, N. Yamashita and M. Fukushima

Journal of Optimization Theory and Applications, 2001, vol. 109, issue 1, No 7, 123-167

Abstract: Abstract 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 split successively the nonsmooth equation into equivalent equations with a particular structure. Based on the splitting, we develop a BFGS method in which the 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 approximate norm descent property. The method is well defined and, under suitable conditions, converges to a KKT point globally and superlinearly without any convexity assumption on the problem.

Keywords: KKT systems; splitting functions; BFGS method; global convergence; superlinear convergence (search for similar items in EconPapers)
Date: 2001
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DOI: 10.1023/A:1017565922109

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