Using a Modified Secant Equation for Unconstrained Optimization

We make some efficient modifications on the modified se-cant equation proposed by Zhang and Xu (2001). Then we introduce modified BFGS method using propose secant equation, and obtain some attractive results in theory and practice. We establish the global conver- gence property of the proposed method without convexity assumption on the objective function. Numerical results on some testing problems from CUTEr collection show the priority of the proposed method to some existing modified secant methods in practice.