An Improved Algorithm For The Gradient Of Liu-Storey Conjugate And Convergence Analysis

The problem of unconstrained optimization is widely used in real life.Nonlin-ear conjugate gradient method is an important method to solve the problem of un-constrained optimization,which has the obvious advantage that the required storage quantity is small and has good convergence properties,so it is especially suitable for solving the problem of large-scale optimization.In the specific use of the Hesfenes-Stiefel(HS)method,Fletcher-Reeves(FR)method,Polak-Ribiere-Polyak(PRP)method and Liu-Storey(LS)method,the main discussion of this paper is the LS method.The LS method has good numerical results in the actual calculation,but its conver-gence is not satisfactory.Therefore,on the basis of the previous scholars'research,this paper analyzes and discusses how to improve the method of LS conjugate gradient and convergence.Mainly includes:1.Through a kind of improved non-monotonous line search,the method of the LS conjugate gradient meets the full decline in the iteration process,and at the same time gives the proof of global convergence.2.A new formula was obtained by correcting the parameter₆)of the LS conjugate gradient method,and an algorithmic framework was established with the new formula.Under the condition of not relying on any line search,it is proved that the iterative directions generated by the algorithm framework established by the new formula meet the sufficient descent condition,and combined with the improved weak Wolfe-Powell line search proposed by other scholars,a new line search is obtained.LS conjugate gradient algorithm,and proves the global convergence of the algorithm.Finally,numerical experiments on the new algorithm show that the improved method is effective.