Using a New Type Quasi-Newton Equation for Unconstrained Optimization

The quasi-Newton equation is the very foundation of an assortment of the quasi-Newton methods. In this paper, we derive a new quasi-Newton equation with a gradient-difference vector which makes full use of both function and gradient value information. The novelty of our method is established on the quadratic approximation of objection function. We analyze the convergence rate of the gradient method under some mild condition. Some numerical simulations are conducted to demonstrate the efficiency of the new methods.