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A note on the global convergence theorem of the scaled conjugate gradient algorithms proposed by Andrei

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Abstract

In (Andrei, Comput. Optim. Appl. 38:402–416, 2007), the efficient scaled conjugate gradient algorithm SCALCG is proposed for solving unconstrained optimization problems. However, due to a wrong inequality used in (Andrei, Comput. Optim. Appl. 38:402–416, 2007) to show the sufficient descent property for the search directions of SCALCG, the proof of Theorem 2, the global convergence theorem of SCALCG, is incorrect. Here, in order to complete the proof of Theorem 2 in (Andrei, Comput. Optim. Appl. 38:402–416, 2007), we show that the search directions of SCALCG satisfy the sufficient descent condition. It is remarkable that the convergence analyses in (Andrei, Optim. Methods Softw. 22:561–571, 2007; Eur. J. Oper. Res. 204:410–420, 2010) should be revised similarly.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Mathematics, Statistics and Computer Sciences, Semnan University, P.O. Box 35195-363, Semnan, Iran

    Saman Babaie-Kafaki

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  1. Saman Babaie-Kafaki
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Correspondence to Saman Babaie-Kafaki.

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Babaie-Kafaki, S. A note on the global convergence theorem of the scaled conjugate gradient algorithms proposed by Andrei. Comput Optim Appl 52, 409–414 (2012). https://doi.org/10.1007/s10589-011-9413-3

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