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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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A rank two algorithm for unconstrained minimization
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by Ronald Bass PDF
Math. Comp. 26 (1972), 129-143 Request permission

Abstract:

A stable second-order unconstrained minimization algorithm with quadratic termination is given. The algorithm does not require any one-dimensional minimizations. Computational results presented indicate that the performance of this algorithm compares favorably with other well-known unconstrained minimization algorithms.
References
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  • B. A. Murtagh & R. W. H. Sargent, A Constrained Minimization Method With Quadratic Convergence, presented at the I. M. A. Conference on Optimization, held at the University of Keele, 1968. R. Fletcher, A New Approach to Variable Metric Algorithms, U.K.A.E.A. Report HL 69/4734.
  • M. J. D. Powell, A survey of numerical methods for unconstrained optimization, SIAM Rev. 12 (1970), 79–97. MR 258253, DOI 10.1137/1012004
  • H. H. Rosenbrock, An automatic method for finding the greatest or least value of a function, Comput. J. 3 (1960/61), 175–184. MR 136042, DOI 10.1093/comjnl/3.3.175
  • H. W. Sorenson, Comparison of some conjugate direction procedures for function minimization, J. Franklin Inst. 288 (1969), 421–441. MR 255026, DOI 10.1016/0016-0032(69)90253-1
  • L. A. Zadeh & C. A. Desoer, Linear System Theory, McGraw-Hill, New York, 1963. H. J. Kelley & G. E. Myers, Conjugate Direction Methods for Parameter Optimization, presented at the 18th Congress of the International Astronautical Federation, Belgrade, Yugoslavia, September 1967.
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Additional Information
  • © Copyright 1972 American Mathematical Society
  • Journal: Math. Comp. 26 (1972), 129-143
  • MSC: Primary 90C30
  • DOI: https://doi.org/10.1090/S0025-5718-1972-0302191-0
  • MathSciNet review: 0302191