A Regularized Limited Memory BFGS method for Large-Scale Unconstrained Optimization and its Efficient Implementations

TL;DR

This paper introduces a regularized L-BFGS method for large-scale unconstrained optimization that enhances robustness and efficiency, demonstrating promising numerical results compared to standard approaches.

Contribution

It proposes a novel regularization technique for L-BFGS, extending its robustness and efficiency with additional techniques like nonmonotone strategies and Wolfe line search.

Findings

The method guarantees global convergence.

Numerical tests show improved robustness.

Efficient in solving large-scale problems.

Abstract

The limited memory BFGS (L-BFGS) method is one of the popular methods for solving large-scale unconstrained optimization. Since the standard L-BFGS method uses a line search to guarantee its global convergence, it sometimes requires a large number of function evaluations. To overcome the difficulty, we propose a new L-BFGS with a certain regularization technique. We show its global convergence under the usual assumptions. In order to make the method more robust and efficient, we also extend it with several techniques such as nonmonotone technique and simultaneous use of the Wolfe line search. Finally, we present some numerical results for test problems in CUTEst, which show that the proposed method is robust in terms of solving number of problems.