Abstract
A conjugate-gradient method for unconstrained optimization, which is based on a nonquadratic model, is proposed. The technique has the same properties as the Fletcher-Reeves algorithm when applied to a quadratic function. It is shown to be efficient when tried on general functions of different dimensionality.
Similar content being viewed by others
References
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.
Fried, I.,N-Step Conjugate-Gradient Minimization Scheme for Nonquadratic Functions, AIAA Journal, Vol. 9, pp. 2286–2287, 1971.
Goldfarb, D.,Variable-Metric and Conjugate-Direction Methods in Unconstrained Optimization, Recent Developments, ACM Proceedings, National Meeting, Boston, Massachusetts, 1972.
Fletcher, R., andReeves, C. M.,Function Minimization by Conjugate Gradients, Computer Journal, Vol. 6, pp. 163–168, 1963.
Cheney, E. W.,Introduction to Approximation Theory, McGraw Hill, New York, New York, 1960.
Storey, C.,Optimization Using Rational Functions, Methods of Operations Research, Vol. 31, pp. 613–616, 1978.
Rosenbrock, H. H.,An Automatic Method for Finding the Greatest and Least Value of a Function, Computer Journal, Vol. 3, pp. 175–184, 1960.
White, B. F., andHolst, W. R., Paper Presented at the Joint Computer Conference, Washington, DC, 1964.
Colville, A. R.,A Comparative Study of Nonlinear Programming Codes, IBM New York Scientific Center, Technical Report No. 320-2949, 1968.
Powell, M. J. D.,An Efficient Method for Finding the Minimum of a Function of Several Variables without Calculating Derivatives, Computer Journal, Vol. 7, pp. 155–162, 1964.
Cornwell, L. W.,An Acceleration Technique Applied to Conjugate-Direction Algorithms for Nonlinear Problems, Paper Presented at the 45th ORSA/TIMS Meeting, Boston, Massachusetts, 1974.
Wolfe, M. A.,Numerical Methods for Unconstrained Optimization: An Introduction, Van Nostrand Reinhold Company, New York, New York, 1978.
Author information
Authors and Affiliations
Additional information
Communicated by L. C. W. Dixon
Rights and permissions
About this article
Cite this article
Tassopoulos, A., Storey, C. A conjugate-direction method based on a nonquadratic model. J Optim Theory Appl 43, 371–381 (1984). https://doi.org/10.1007/BF00934461
Issue Date:
DOI: https://doi.org/10.1007/BF00934461