Extended conjugate-gradient methods with restarts
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Three variants of the classical conjugate-gradient method are presented. Two of these variants are based upon a nonlinear function of a quadratic form. A restarting procedure due to Powell, and based upon some earlier work of Beale, is discussed and incorporated into two of the variants. Results of applying the four algorithms to a set of benchmark problems are included, and some tentative conclusions about the relative merits of the four schemes are presented.
Key WordsNonlinear optimization conjugate-gradient methods numerical methods computing methods mathematical programming nonlinear programming
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- 1.Powell, M. J. D.,Some Convergence Properties of the Conjugate Gradient Method, Mathematical Programming, Vol. 11, pp. 42–49, 1976.Google Scholar
- 2.Boland, W. R., Kamgnia, E. R., andKowalik, J. S.,A Conjugate Gradient Optimization Method Invariant to Nonlinear Scaling, Journal of Optimization Theory and Applications, Vol. 27, No. 2, 1979.Google Scholar
- 3.Fried, I.,N-step Conjugate Gradient Minimization Scheme for Nonquadratic Functions, AIAA Journal, Vol. 9, pp. 2286–2287, 1971.Google Scholar
- 4.Spedicato, E.,A Variable Metric Method for Function Minimization Derived from Invariancy to Nonlinear Scaling, Journal of Optimization Theory and Applications, Vol. 20, pp. 315–329, 1976.Google Scholar
- 5.Powell, M. J. D.,Restart Procedures for the Conjugate Gradient Method, Atomic Energy Research Establishment, Harwell, England, Report No. CSS-24, 1975.Google Scholar
- 6.Beale, E. M. L.,A Derivation of Conjugate Gradients, Numerical Methods for Nonlinear Optimization, Edited by F. A. Lootsma, Academic Press, New York, New York, pp. 39–44, 1972.Google Scholar
- 7.Spedicato, E.,Recent Developments in the Variable Metric Method for Nonlinear Unconstrained Optimization, Towards Global Optimization, Edited by L. W. Dixon and G. P. Szegö, North-Holland, Amsterdam, pp. 182–195, 1975.Google Scholar