A Regularized Limited Memory BFGS method for Large-Scale Unconstrained Optimization and its Efficient Implementations
This work addresses efficiency and robustness challenges in optimization algorithms for researchers and practitioners in computational mathematics, though it appears incremental with hybrid techniques.
The paper tackles the issue of high function evaluations in the standard L-BFGS method for large-scale unconstrained optimization by proposing a regularized L-BFGS approach, showing global convergence and improved robustness in numerical tests on CUTEst problems.
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.