Abstract
An algorithm is proposed for minimizing certain niceC 2 functionsf onE n assuming only a computational knowledge off and∇f. It is shown that the algorithm provides global convergence at a rate which is eventually superlinear and possibly quadratic. The algorithm is purely algebraic and does not require the minimization of any functions of one variable.
Numerical computation on specific problems with as many as six independent variables has shown that the method compares very favorably with the best of the other known methods. The method is compared with theFletcher andPowell method for a simple two dimensional test problem and for a six dimensional problem arising in control theory.
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References
Goldstein, A.A.: On steepest descent. SIAM J. on Control, A,3, 1, 147–151 (1965).
Kantorovich, L. V., andG. P. Akilov: Functional analysis in normed spaces. New York: Macmillan 1964.
Fletcher, R., andM. J. D. Powell: A rapidly convergent descent method for minimization. Computer J. p. 163–168, July 1963.
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Supported by Air Force grant AF-AFO SR-93 7-65 and Boeing Scientific Research Laboratories.
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Goldstein, A.A., Price, J.F. An effective algorithm for minimization. Numer. Math. 10, 184–189 (1967). https://doi.org/10.1007/BF02162162
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DOI: https://doi.org/10.1007/BF02162162