Using a modied secant equation for unconstrained optimization

Abstract

We make some ecient modications on the modied secant equation proposed by Zhangand Xu (2001). Then we introduce modied BFGS method using propose secant equation,and obtain some attractive results in theory and practice. We establish the global con-vergence property of the proposed method without convexity assumption on the objectivefunction. Numerical results on some testing problems from CUTEr collection show the pri-ority of the proposed method to some existing modied secant methods in practice