Abstract
The theory of unconstrained optimization has led to the development of a large class of iterative methods that reduce to conjugate direction methods when they are applied to quadratic functions. The purpose of this paper is to give a generalization of conjugate directions to nonquadratic functions.
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Fox, L., Huskey, H. D., andWilkinson, J. H.,Notes on the Solution of Algebraic Linear Simultaneous Equations, Quarterly Journal of Mechanics and Applied Mathematics, Vol. 1, pp. 149–173, 1948.
Hestenes, M. R., andStiefel E.,The Method of Conjugate Gradients for Solving Linear Systems, Journal on Research of the National Bureau of Standards, Vol. 49, pp. 409–436, 1952.
Davidon, W. C.,Variable-Metric Method for Minimization, Atomic Energy Commission, Argonne National Laboratory, Argonne, Illinois, Research and Development Report No. ANL-5990, 1959.
Fletcher, R., andPowell, M. J. D.,A Rapidly Convergent Method for Minimization, Computer Journal, Vol. 6, pp. 163–168, 1963.
Huang, H. Y.,Unified Approach to Quadratically Convergent Algorithms for Function Minimization, Journal of Optimization Theory and Applications, Vol. 5, No. 6, 1970.
Kobayashi, S., andNomizu, K.,Foundations of Differential Geometry, Vol. 1, Interscience, New York, New York, 1963.
McDowell, D. G.,A Characterization of the Minimizer of a Function, Journal of Optimization Theory and Applications, Vol. 25, No. 1, 1978.
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Communicated by H. Y. Huang
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McDowell, D.G. Generalized conjugate directions for unconstrained function minimization. J Optim Theory Appl 41, 523–531 (1983). https://doi.org/10.1007/BF00934640
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DOI: https://doi.org/10.1007/BF00934640