Limited memory BFGS method based on a high-order tensor model

Abstract

This paper is aimed to employ a modified quasi-Newton equation in the framework of the limited memory BFGS method to solve large-scale unconstrained optimization problems. The modified secant equation is derived by means of a forth order tensor model to improve the curvature information of the objective function. The global and local convergence properties of the modified LBFGS method, on uniformly convex problems are also studied. The numerical results indicate that the proposed limited memory method is superior to the standard LBFGS method.