The Analysis And Research Of The Quasi-newton Algorithm

Quasi-Newton algorithm has been proved to be the most effective and most sophisticated one for solving unconstrained optimization problem. In this paper, we analyze the quasi-newton equation further based on the previous works of quasi-newton algorithm and put forward the modified quasi-newton equation to improve the quasi-newton algorithm combining with correction formula and search criteria. Finally, a new quasi-newton algorithm was proposed by combining quasi-newton algorithm with other algorithms. There are three parts in this thesis.Firstly, we introduced the background and related content and research situation of quasi-newton algorithm. In the second chapter, we introduced the basic knowledge, including the correction formula, the line search method, convergence, etc.Secondly, we used weighted average method to get one kind of effective new quasi-newton algorithm, with previous quasi-newton equation. Under some suitable conditions, we proved the global convergence. At last, through numerical experiments, our algorithm is efficient for unconstrained optimization problem.Thirdly, by adding parameters, we generalized the existing quasi-newton equation. And under the non-monotone linear search technique and some suitable conditions, we proved the global convergence of the new non-monotone quasi-newton algorithm. Finally, through numerical experiments, our algorithm was efficient.Finally, a combined algorithm was proposed by combining the new quasi-newton algorithm in third chapter with the structure secant method. Utilizing the gradient information and the function value of the objective function. And using the Wolfe linear search technique, under some suitable conditions, we proved that the new algorithm has global and superlinear convergence.