Multidimensional Filter With Two Iterative Algorithm

Unconstrained optimization problem is one of the common optimization problems,and the ways to solve the problems are various.One of which is the Newton method.But Newton method has certain limitations,so a series of correction about Newton method are emerged.Based on a lot of research achievements of predecessors, combining the Newton method for correcting method with the1999Zhang Jianzhong on multiple phase difference gradient and introducing the function value information method, the modified two step quasi Newton method is emerged.Then,uniting the modified.Newton method and filter method,a new algorithm is obtained.And in some assumptions premise, we prove global convergence for new algorithm, and report some preliminary numerical results.