Two Kinds Of Conjugate Gradient Methods For Solving Nonlinear Equations

The optimization problem is a very important research direction in the disciplines of Operations Research and Cybernetics.The nonlinear optimization problem is also an important part of the optimization problem.There are many nonlinear optimization problems in reality,such as weather forecasting,petroleum exploration,and engineering design.The general solutions of nonlinear equations are conjugate gradient method,Newton method,quasi-Newton method,etc.In this paper,three terms of conjugate gradient method and projection conjugate gradient method are mainly studied for solving nonlinear equations.First,in the first half of the article,some research backgrounds and their significance related to this article are introduced,as well as the research status at home and abroad,the basic concepts of optimization problems,etc.The second part of this paper presents two improved conjugate gradient algorithms,Combined projection technology,solving the problem of equations by solving it into an unconstrained problem.Under certain conditions,we proves the sufficient descent of the algorithm,automatic trust region properties,and global convergence.Numerical experiments are given later in the chapter,and Compared with the original algorithm,there are better numerical results.