On the convergence of \(s\)-dependent GFR conjugate gradient method for unconstrained optimization
One of the effective methods for solving the optimization problem is conjugate gradient method. For line search, the Fletcher-Reeves (FR) conjugate gradient method was considered by \textit{Y. H. Dai} and \textit{Y. Yuan} [IMA J. Numer. Anal. 16, No. 2, 155--164 (1996; Zbl 0851.65049)]. They obtained a generalized FR method which is called GFR method. Based on the generalized FR method, the authors present an \(s\)-dependent GFR method for unconstrained optimization problem. They also obtain two different kinds of estimations of upper bounds of a parameter which fulfils the FR-formula. Using several step-size rules, the global convergence of \(s\)-dependent GFR conjugate method is proved.
scientific article; zbMATH DE number 6904320
scientific article