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A regularized limited-memory BFGS method for unconstrained minimization problems

Shinji Sugimoto(sugimoto***at***amp.i.kyoto-u.ac.jp)
Nobuo Yamashita(nobuo***at***i.kyoto-u.ac.jp)

Abstract: The limited-memory BFGS (L-BFGS) algorithm is a popular method of solving large-scale unconstrained minimization problems. Since L-BFGS conducts a line search with the Wolfe condition, it may require many function evaluations for ill-posed problems. To overcome this difficulty, we propose a method that combines L-BFGS with the regularized Newton method. The computational cost for a single iteration of the proposed method is the same as that of the original L-BFGS method. We show that the proposed method has global convergence under the usual conditions. Moreover, we present numerical results that show the robustness of the proposed method.

Keywords: unconstrained minimization problems, L-BFGS, regularized Newton methods

Category 1: Nonlinear Optimization (Unconstrained Optimization )

Citation: Technical report, Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Japan, 2014.

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Entry Submitted: 08/04/2014
Entry Accepted: 08/04/2014
Entry Last Modified: 08/04/2014

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