An Adaptive Quasi-Newton Equation for Unconstrained Optimization

The quasi-Newton methods is an effective and interesting methods and their good accuracy for unconstrained optimization. In this paper, a novel quasi-Newton equation is given based on the quadratic model, and quasi-Newton methods are constructed on it. To motivate the conventional quasi-Newton equation, which used both objective function and gradient information. Under Wolfe circumstances, the global convergence of an algorithm is shown for generic functions. Numerical results show that the new method is superior to the BFGS - method.