Fixed Newton Method In Optimization Theory Research

In a lot of methods for solving unconstrained optimization problems, modified Newton method with its global convergence and convergence speed advantages, received extensive attention of people. However, a considerable amount of research on modified Newton method is based on monotone line search technique, using the nonmonotone line search technique is rare. In view of this, this paper mainly studies the nonmonotone modified Newton method in optimization method. First, we introduce a modified Newton method for solving unconstrained optimization problems of related concepts, and in this paper modified Newton method and line search technique, on the basis of the research status and progress, we summarized the main work done in this paper. Second, according to Newton’s method in the process of solving general non-convex function minimum, a reduced order modified Newton method. The method makes full use of the iteration points target function of the first and second order information, appropriate selection search direction, Newton’s method is the least squares problem under mild conditions to establish the global convergence of the algorithm, and the convergence rate of estimation is given.