Two Kinds Of Nonlinear Conjugate Gradient Algorithm

With the progress of science and technology and the rapid developmen-t of society,the increasing problems and decisions in practice are prompting people to study the optimization method.This method mainly puts forward var-ious scientific schemes for different problems,and strives to find the optimal decision-making scheme.In real life,optimization methods are widely used in finance,trade,engineering management and other fields.Therefore,optimiza-tion methods have important significance and research value.This dissertation research some algorithms about solving large-scale unconstrained optimization problems.A three-term conjugate gradient algorithm based on double parameter s-caled BFGS update is presented to solve large-scale unconstrained optimization problems.Algorithm adopt the MWWP line search obtain step size?_k.d_kis obtained by a symmetrical Perry matrix which contains two positive parameter-s and gradient,and the sufficient descent property of the generated directions holds independent of the presented line search technique.The algorithm intro-duces a paraboloid to correct the influence of the failed point in iteration,which is regarded as the projection plane,and the next iteration point x_k+1is generat-ed by the new projection technology.Under a modified WWP line search,the new algorithm can guarantee global convergence and performs better than other algorithms in numerical experiments.A modified Dai-Liao conjugate gradient method based on the new con-jugacy condition is presented to solve large-scale unconstrained optimization problems.A new conjugacy condition is established based on two quasi-Newton equations.Based on the presented conjugacy condition,the modified Dai-Liao conjugate gradient method considers both the gradient and function value infor-mation.Under some suitable assumptions,the global convergence is achieved for the modified Dai-Liao conjugate gradient method.Numerical experiments on unconstrained optimization problems and image restoration problems are conducted,and the numerical results show that our method is efficient.