Based On The New Quasi-newton Equation Improved Bfgs Method

The BFGS method is generally considered to be the most effective among othervariable metric methods for unconstrained optimization. But our pioneers have madegreat efforts to find out modified BFGS method which is not only possessing the sameconvergence properties but also superior than the BFGS method.With the framework of the tool of Byrd and Nocedal, Liao aiping gives amodified BFGS method with better ability to correct large eigenvalues. Liao showsthat under certain circumstances this modified method has the global and superlinearconvergence properties. Based on the Quasi-Newton funtion propsed by Wei zengxin, Xiao yunhai gives another modified method. With Wolfe line search, he showsthat the modified method has the global convergence properties and the numericalresults are better. Based on Liao's method and the Quasi-Newton function proposedby himself, Wei also gives a new modified method with the general Wolfe linesearch. Under suitable conditions, he establishes global and superlinear convergenceand the better numerical result.In this paper, we propose a new modified BFGS method based on Liao's modifiedmethod, Xiao's modified BFGS method and Wei's modified BFGS method. Thismodified method can be regarded as an implementation technique. By choosing theproper parameters, we can prove that the new method has global and superlinearconvergence properties under suitable conditions. At last, the numerical results arealso presented, which show that the proposed algorithm is efficient for unconstrainedoptimization problems.