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.

Keywords:

• conjugate gradient algorithm
• sufficient descent condition
• line search
• global convergence

Acknowledgements

This research was in part supported by a grant from IPM (No. 90900023), and in part by the Research Council of Semnan University. The author is grateful to the anonymous reviewers for their valuable suggestions that helped to improve the presentation.