1. On the Method of Shortest Residuals for Unconstrained Optimization.
- Author
-
Pytlak, R. and Tarnawski, T.
- Subjects
CONJUGATE gradient methods ,APPROXIMATION theory ,NUMERICAL solutions to equations ,ITERATIVE methods (Mathematics) ,MATHEMATICAL optimization ,ALGORITHMS ,STOCHASTIC convergence ,NUMERICAL analysis ,CALCULUS of variations - 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. [ABSTRACT FROM AUTHOR]
- Published
- 2007
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