Conjugate Gradient Method And Its Application

The conjugate gradient method has played an efficient role in solving unconstrained optimization,especially in solving large-scale nonlinear optimization. Recently,domestic and overseas scholars proposed a cass of new nonlinear conjugate gradient methods,which use both available gradient and function value information.However,they have good numerical experiments.At the first,this paper introduced the referring conception of unconstrained nonlinear optimization method and some main and simple solves of the problem had been supplied, indicate the basic referring definition and introduction about conjugate gradient.Based on the new quasi-newton equation with the function information,the paper proposed a modified PRP conjugate gradient method and a modified DY conjugate gradient method.Aan prove that they are Global convergence under the strong wolf line search.The numerical results show that the new algorithm is efficient.In recent years, the inverse problem is widely used in geophysics, life science, and remote sensing technology, materials science, signal processing, so it has a wide and important application. And it also popular in the applied mathematics and science subjects.The third chapter mainly introduces the basic concepts of the inverse problem some several optimization method to solve the inverse problem. And the paper also proposed the idea the solve the inverse problem with the conjugate gradient method which with the function information.