Optimal Scaling Parameters for Spectral Conjugate Gradient Methods

Amin Fahs (), Hassane Fahs () and R. Dehghani ()
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Amin Fahs: University of Strasbourg, Laboratory ICube, CS 10413 - F-67412
Hassane Fahs: Lebanese International University
R. Dehghani: Yazd University

SN Operations Research Forum, 2022, vol. 3, issue 2, 1-13

Abstract: Abstract To improve upon numerical stability of the spectral conjugate gradient methods, two adaptive scaling parameters are introduced. One parameter is obtained by minimizing an upper bound of the condition number of the matrix involved in producing the search direction and the other one is obtained by minimizing the Frobenius condition number of the matrix. The proposed methods are shown to be globally convergent, under appropriate conditions. A comparative testing of the proposed methods and some efficient spectral conjugate gradient methods shows the computational efficiency of the proposed methods.

Keywords: Unconstrained optimization; Spectral conjugate gradient method; Condition number; Global convergence; 90C53; 49M37; 65K05 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s43069-022-00141-z

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