Erratum to: Scaled memoryless BFGS preconditioned conjugate gradient algorithm for unconstrained optimization

Abstract

In Andrei [Scaled memoryless BFGS preconditioned conjugate gradient (CG) algorithm for unconstrained optimization, Optim. Meth. Softw. 22(4) (2007), pp. 561–571], an efficient CG algorithm has been proposed for solving unconstrained optimization problems. However, due to a wrong inequality used in Andrei to show the sufficient descent property for the search directions, the proof of Theorem 2, the global convergence theorem, is incorrect. In what follows, the necessary corrections will be mentioned. Throughout, we use the same notations as in Andrei.