A New Inexact Line Search Conjugate Gradient Method

Optimization is a strong disciplines applied. In recent years, with the development of computer and practical issues need, large-scale optimization problems are given more and more attention. Thus, finding high performance algorithms in nonlinear optimization is becoming very heated research topic. Quasi-Newton algorithm and conjugate gradient algorithm are two effective algorithms,particularly conjugate gradient algorithm.In this paper, we presents inexact line search and conjugate gredient methods for unconstrained optimization. Based on the traditional Wolfe line search.we proposed a new inexact line search. In paper [1], it is noted in the convergence analysis of the Fletcher-Reeves algorithm under the Wolfe line search, the conditions σ ≤ 1/2 is not improved. However, under the new line search, in the case of the parameter without the restriction σ ≤ 1/2, we prove the global convergence of the Fletcher-Reeves method. Numerical experiments demonstrated the effectiveness of the new line search. Then, we tried to turn this line search applications to other conjugate gradient method.In chapter 1, we introduce the development of optimization and some extensive optimality conditions to determine the optimum solution. We review several extensive derivative descent methods for unconstrained programming.In chapter 2, we propose a new inexact line search and demonstrated its feasibility. We get promotion Zoutendijk condition. And then we made a comparison of the traditional Wolfe line search.In chapter 3, we will mainly consider the Fletcher-Reeves algorithm under the new line search. Compared the Wolfe line search in the larger context of the parameters we prove the global convergence of the Fletcher-Reeves method. Moreover, the subsequent results of the numerical experiments are described more effective than traditional algorithms.In chapter 4, we will try to promote this line search to other conjugate gradient methods without the sufficient descent condition.