Two Types Of Modified Hybrid Conjugate Gradient Methods And Their Convergence Analysis

The Conjugate gradient method has properties of small storage space and simple iteration form in numerical calculation,which is widely used in many fields,for instance,weather prediction,economy and finance,transportation and so on.Therefore,it is of great theoretical significance and practical value to research the conjugate gradient method with good convergence and numerical performance.Based on the hybrid conjugate gradient method,this paper studies the solution of unconstrained optimization problems and constrained nonlinear monotone equations.For unconstrained optimization problems,inspired by the conjugate gradient algorithm proposed by Stiefeland Hestenes,this paper proposes an improved hybrid conjugate gradient method for unconstrained optimization,the improved method generate a descent search direction independent of line search technique.Under certain conditions,it is proved that the algorithm is globally convergent based on line search technology.The robustness and effectiveness of the proposed algorithm are verified by numerical experiments.For nonlinear monotone equations with constraints,this paper proposes an improved accelerated hybrid conjugate gradient projection algorithm based on hybrid conjugate gradient method,hyperplane projection technique and step acceleration method.The algorithm only uses the gradient information of the objective function not the Jacobin matrix value of the function,which effectively improves the efficiency of numerical calculation.The algorithm’s search direction satisfies the famous D-L conjugate condition,and satisfies the Newton direction under certain conditions.The algorithm has sufficient descent and trust region properties independent of projection and line search techniques.It is proved that the algorithm has global convergence under appropriate assumptions.Numerical experiments demonstrate that the algorithm can have good numerical performance in solving large-scale nonlinear monotone equations.At the end of this paper,the two new algorithms are summarized briefly,and some prospects for further research on this subject are put forward.Figure [7] Table [7] Reference [66]...