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Symposium on Optimization pp 151–158Cite as

Accelerated gradient projection

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Part of the book series: Lecture Notes in Mathematics ((LNM,volume 132))

Abstract

A version of the gradient projection algorithm is proposed for use with nonlinear constraints. Compatibility with the Davidon process is examined and arguments on terminal phase convergence are given.

This research was performed under NASA Contracts NAS 9-7805 with NASA MSC, Houston, Texas, and NAS 12-656 with NASA ERC, Cambridge, Massachusetts. Presented at the Colloquium on Optimization, Nice, France, June 29–July 5, 1969.

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References

  1. Davidon, W.C.; "Variable Metric Method for Minimization," Argonne National Laboratory Report ANL-5990 Rev., November 1959.

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  2. Fletcher, R. and Powell, M.J.D.; "A Rapidly Convergent Descent Method for Minimization," British Computer Journal, July 1963.

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  3. Goldfarb, D. and Lapidus, L.; "A Conjugate Gradient Method for Non-linear Programming," A.I.Ch.E. 61st National Meeting, Houston, Texas, February 1967.

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  4. Kelley, H.J., Denham, W.F., Johnson, I.L. and Wheatley, P.O.; "An Accelerated Gradient Method for Parameter Optimization with Nonlinear Constraints," J. Astronautical Sciences, July–August 1966.

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  5. Rosen, J.B.; "The Gradient Projection Method for Nonlinear Programming, Part I: Linear Constraints," J. SIAM, March 1960; "Part II: Nonlinear Constraints," J. SIAM, December 1961.

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Author information

Authors and Affiliations

  1. Analytical Mechanics Associates, Inc., Jericho, N.Y., USA

    Henry J. Kelley & Jason L. Speyer

Authors
  1. Henry J. Kelley
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  2. Jason L. Speyer
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Editor information

A. V. Balakrishnan M. Contensou B. F. de Veubeke P. Krée J. L. Lions N. N. Moiseev

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© 1970 Springer-Verlag

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Kelley, H.J., Speyer, J.L. (1970). Accelerated gradient projection. In: Balakrishnan, A.V., Contensou, M., de Veubeke, B.F., Krée, P., Lions, J.L., Moiseev, N.N. (eds) Symposium on Optimization. Lecture Notes in Mathematics, vol 132. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0066680

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  • DOI: https://doi.org/10.1007/BFb0066680

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-04921-0

  • Online ISBN: 978-3-540-36275-3

  • eBook Packages: Springer Book Archive

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