A Nonmonotone Modified BFGS Algorithm for Nonconvex Unconstrained Optimization Problems

Abstract

In this paper, a modified BFGS algorithm is proposed to solve unconstrained optimization problems. First, an update formula is recommended to approximate Hessian matrix based on a modified secant condition. Second, thanks to the remarkable nonmonotone line search properties, this work takes advantages of nonmonotone line search strategies. Under some mild conditions, the global convergence properties of the algorithm are established without convexity assumption on the objective function. By the numerical experiments, it is established that the suggested algorithm is promising.