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

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 proper...

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Vydáno v:	Computational optimization and applications Ročník 52; číslo 2; s. 409 - 414
Hlavní autor:	Babaie-Kafaki, Saman
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Boston Springer US 01.06.2012 Springer Nature B.V
Témata:	Algorithms Analysis Approximation Computer science Conjugate gradients Convergence Convex and Discrete Geometry Descent Eigenvalues Iterative methods Management Science Mathematics Mathematics and Statistics Operations Research Operations Research/Decision Theory Optimization Optimization algorithms Proving Searching Statistics Studies Theorems Line search Sufficient descent condition Global convergence Scaled conjugate gradient algorithm
ISSN:	0926-6003, 1573-2894
On-line přístup:	Získat plný text
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Shrnutí:	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.
Bibliografie:	SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 14 ObjectType-Article-2 content type line 23
ISSN:	0926-6003 1573-2894
DOI:	10.1007/s10589-011-9413-3