An arc-search BFGS algorithm for unconstrained nonlinear optimization problems

Abstract

The classical BFGS algorithm performs excellently for convex optimization problems. However, for non-convex problems, the classical BFGS method may fail to converge reliably. To overcome this limitation, researchers have developed modified BFGS methods that are applicable to both convex and non-convex optimization problems. Among these methods, a robust BFGS algorithm has been shown to achieve global convergence and fast local convergence, with a superlinear convergence rate, for both convex and non-convex nonlinear optimization problems under mild assumptions. In this paper, we propose an arc-search BFGS algorithm that aims to further improve the computational efficiency of the robust BFGS method while preserving its desirable convergence properties. Numerical experiments are carried out, and performance comparisons between the proposed algorithm and state-of-the-art algorithms are reported to demonstrate the advantages of the arc-search BFGS algorithm.