A New Class Of Quasi-newton Algorithm And Its Convergence

The BFGS method is a well-known quasi-Newton method for solving unconstrained opti-mization problems.The method only use the objective function and it's first-order derivative value without forming Hessian matix.Moreover,the method possesses the advantage which is quickly convengent speed and good numerical result.A class of modified BFGS algorithm suitable for traditional quasi-newton equation was gen-eralized to the new quasi-newton equation,and a class of modified BFGS algorithm based on new quasi-newton equation was obtianed by Wang Haibin[14].Wang shows the modified method has the global and local superlinear convergence properties. Based on the modified quasi-Newton. equation proposed by Wei Zengxin[13], he gives a new modified BFGS method with a gen-eral Wolfe line search. Under some suitable conditions,he establishes global and superlinear convergence and better numerical result.Under the inspiration of the Wang Haibin[14],we based on the objective function of local non-quadratic model approximation,take Bk+1 to The use of the objective function of the third-order and fourth-order tensor,get a new tk.At the same time, we present a new modified BFGS method based on the new quasi-Newton equation Wei Zengxin[13]proposed.Under some suitable conditions,we prove the global and local q-superlinear convergence of our method.At last,numerical results are also presented.Experiments show that the algorithm is effective.