A globally convergent BFGS method with nonmonotone line search for non-convex minimization

Authors:
Yunhai Xiao;Huijuan Sun;Zhiguo Wang
Affiliations:
Department of Mathematics, Nanjing University, Nanjing, 210093, PR China and Institute of Applied Mathematics, College of Mathematics and Information Science, Henan University, Kaifeng, 475004, PR ...;Institute of Applied Mathematics, College of Mathematics and Information Science, Henan University, Kaifeng, 475004, PR China;Institute of Applied Mathematics, College of Mathematics and Information Science, Henan University, Kaifeng, 475004, PR China
Venue:
Journal of Computational and Applied Mathematics
Year:
2009

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Abstract

In this paper, we propose a modified BFGS (Broyden-Fletcher-Goldfarb-Shanno) method with nonmonotone line search for unconstrained optimization. Under some mild conditions, we show that the method is globally convergent without a convexity assumption on the objective function. We also report some preliminary numerical results to show the efficiency of the proposed method.