Department of Applied Mathematics & Physics, Kyoto University

Technical Report 2014-001 (August 5, 2014)

A regularized limited-memory BFGS method for unconstrained minimization problems
by Shinji SUGIMOTO and Nobuo YAMASHITA

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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.