Research On Sufficient Descent Several Classes Of Conjugate Gradient Method

Because of these excellent features such as simple algorithm,easy to program,less needs for storage,etc,Conjugate gradient method is often used as an important method to solve the problem of large-scale nonlinear unconstrained optimization.And in many areas of real life,the method is frequently used and effective.This paper introduces the research status of classical conjugate gradient method,modified conjugate gradient method,mixed conjugate gradient method and spec-tral conjugate gradient method.On the basis of previous scholars' research,the conjugate gradient method is further analyzed and discussed.We get the following research results:Firstly,a class of sufficiently descent spectral conjugate gradient method was put forwa.rd,which satisfies descent condition.Besides,the method possesses the advantage of FR,WYL and PPR.Then,the global convergence of a new hybrid spectral conjugate gradient method is proved with the reduction to absurdity under the Wolfe line search.Finally,iterative times and computing time are compared among the new algorithm and the existing WYL and FR algorithms.The compar-ison results show that the new algorithm is superior to the ot,her algorithms.The global convergence and the numerical superiority indicate that the new algorithm is an effective algorithm which is worth studying.On the basis of the modified conjugate gradient method,a kind of WFR spec-tral conjugate gradient method is proposed,and the sufficient descent property is always possessed without any line search.Besides,the new spectral conjugate gra-dient method possesses global convergence,which was proved under the standard Wolfe line search.We conducted a series of numerical experiment test,the results indicate that the new algorithm is superior to the VFR method.