Conjugate Gradient Method For Unconstrained Optimization Problems And Constrained Nonlinear Equations

Conjugate gradient method is a class of effective methods for solve unconstrained optimization problems.It has been widely studied and concerned,and has been applied to practical problems.In recent years,the application of conjugate gradient method to nonlinear equations has also made some progress.Based on the existing research results,this paper proposes two conjugate gradient algorithms.They are used to solve general unconstrained optimization problems and nonlinear equations,and the sufficient descent and global convergence of the algorithm are obtained.Finally,the effectiveness of the algorithm is verified by numerical experiments.In Chapter 1,we mainly introduces the research background,research significance and research status at home and abroad.In Chapter 2,we introduce the related concepts and basic properties of optimization problems.In Chapter 3,we do some analyze and sort out about existing conjugate gradient methods to solve unconstrained problems and propose a new conjugate gradient method.Under the condition of strong Wolfe line search,the theoretical properties such as sufficient descent and global convergence of the algorithm are analyzed.Finally,some numerical experiments are carried out on some examples,and the results show that the proposed algorithm has good numerical effect.In Chapter 4,we do some analyze and sort out about existing conjugate gradient methods for solving constrained nonlinear equations.Combined with the idea of projection method,a new conjugate gradient projection algorithm is proposed to solve constrained nonlinear equations under suitable line search technique.The theoretical properties of the algorithm,such as sufficient descent and global convergence,are analyzed and preliminary numerical experiments are carried out.