Modified Quasi-Newton Method via Linear Gradient Flow System

This paper introduces an efficient method for unconstrained optimization based on approximating the gradient flow derived from the objective function. The proposed method uses linear approximation and some quasi-Newton update to approximate the gradient flow, which leads to a modified quasi-Newton BFGS update. An implementation of the proposed method under the line search approach is considered. Numerical results demonstrate that the modified BFGS method is more effective to standard BFGS method.