A New Class Of Quasi-newton Algorithm And Its Convergence

The BFGS method is the most effective of the quasi-Newton methods for solving unconstrained minimization problems.In recent 20 years,many authors have made great efforts to study the modified BFGS methods which not only possess the good properties of convergence but also superior then the usual BFGS method from the computation point of view.With the anslysis tool Byrd and Nocedal proposed,Liao aiping gives a modified BFGS method with a better ability to correct large eigenvalues.Liao shows the modified method has the global and local superlinear convergence properties.Based on the modified quasi-Newton equation proposed by Wei zeng xin,he gives a new modified BFGS method with a general Wolfe line search.Under some suitable conditions,he establishes global and superlinear convergence and better numerical result.In this paper,we present a new modified BFGS method based on the new quasi-Newton equation Hiroshi Yabe et.al proposed.Under some suitable conditions,we prove the global and local q-superlinear convergence of our method.At last,numerical results are also presented.Comparing with the usual BFGS method,our method is efficient for unconstrained optimization.