| The solution of nonlinear equations is the most basic problem in nonlinear optimization problems.In the real world,nonlinear equations are widely used in engineering practice,information security,and economics and so on.The classical methods for solving nonlinear equations have gradient method,Newton method,quasi-Newton method,conjugate gradient method and so on.Two kinds of conjugate gradient methods for solving nonlinear equations are studied in this paper.For nonlinear equations,this paper presents a search direction that combines three-term LS conjugate gradient method and convex combinations formulas.The search direction has sufficient descent and trust region properties without any line search.In addition,based on accelerated step size and backtracking line search technology,this paper proposes a new conjugate gradient algorithm,and the global convergence property is established.The final numerical experiment also show that the algorithm is superior to the comparative conjugate gradient algorithm for large-scale nonlinear equations and image restoration problems.To solve monotone nonlinear equations,we present an accelerated conjugate gradient algorithm based on the three-term PRP conjugate gradient method,the accelerated step length and the hyperplane projection technique in this paper.It has the following properties:(i)All search directions generated by this algorithm not only have sufficient descent but also satisfy trust region property;(ii)Use a derivative-free line search technique to obtain step length;(iii)_k(29)0,then use the accelerated step length to get the next iteration point,if the point meets the judgment condition,then continue with the next step;Otherwise,a hyperplane projection technique is used to get the next iteration point;(iv)Under appropriate conditions,it is proved that the algorithm has global convergence property.Finally,the numerical comparison with other conjugate gradient methods shows that the new algorithm has better numerical effect. |
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