On the Method of Shortest Residuals for Unconstrained Optimization

R. Pytlak () and T. Tarnawski
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R. Pytlak: Military University of Technology
T. Tarnawski: Military University of Technology

Journal of Optimization Theory and Applications, 2007, vol. 133, issue 1, No 7, 99-110

Abstract: Abstract The paper discusses several versions of the method of shortest residuals, a specific variant of the conjugate gradient algorithm, first introduced by Lemaréchal and Wolfe and discussed by Hestenes in a quadratic case. In the paper we analyze the global convergence of the versions considered. Numerical comparison of these versions of the method of shortest residuals and an implementation of a standard Polak–Ribière conjugate gradient algorithm is also provided. It supports the claim that the method of shortest residuals is a viable technique, competitive to other conjugate gradient algorithms.

Keywords: Conjugate gradient algorithms; Unconstrained optimization (search for similar items in EconPapers)
Date: 2007
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DOI: 10.1007/s10957-007-9194-0

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