ON　THE　CONVERGENCE　OF　CONJUGATE　GRADIENT　METHODS INVARIANT TO　NONLINEAR　SCALING

ON THE CONVERGENCE OF CONJUGATEGRADIENT METHODS INVXRIANT TONONLINEAR SCALING

ＯＮＴＨＥＣＯＮＶＥＲＧＥＮＣＥＯＦＣＯＮＪＵＧＡＴＥＧＲＡＤＩＥＮＴＭＥＴＨＯＤＳＩＮＶＡＲＩＡＮＴＴＯＮＯＮＬＩＮＥＡＲＳＣＡＬＩＮＧＤＥＮＧＮａｉｙａｎｇ；ＬＩＺｈｅｎｇｆｅｎｇ（ＤｉｖｉｓｉｏｎｏｆＢａｓｉｃＳｃｉｅｎｃｅ，ＢｅｉｊｉｎｇＡｇ...

Abstract:In order to construct more efficient methods for unconstrained optimizationproblems, several authors have considered more general functions than quadratic functionsas a basis for conjugate gradient method in recent years. Although interesting numericalexperiments have been obtained by using the new methods, their convergence has remained an open problem even when line searches are exact. Under some assumptions, twoglobal convergence theorems for the extended Fletcher-Reeves and Polak-Ribiere methodsproposed in [1] are given in this paper.