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Elements of Large Scale Mathematical Programming Part II: Synthesis of Algorithms and Bibliography

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  • Arthur M. Geoffrion

    (University of California, Los Angeles)

Abstract

The problem manipulations and solution strategies of Part I of this paper are now further illustrated by combining them in various ways to yield several known algorithms. The main object is not an exposition of these algorithms, although this is certainly important; rather, we wish to focus on the principal patterns in which manipulations and strategies can be assembled. These patterns constitute the real common denominators in the literature on large-scale programming. See Table 2 in Part I.

Suggested Citation

  • Arthur M. Geoffrion, 1970. "Elements of Large Scale Mathematical Programming Part II: Synthesis of Algorithms and Bibliography," Management Science, INFORMS, vol. 16(11), pages 676-691, July.
    • Handle: RePEc:inm:ormnsc:v:16:y:1970:i:11:p:676-691
    DOI: 10.1287/mnsc.16.11.676
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    Cited by:

    1. Xiang Li & Asgeir Tomasgard & Paul Barton, 2012. "Decomposition strategy for the stochastic pooling problem," Journal of Global Optimization, Springer, vol. 54(4), pages 765-790, December.
    2. Rahmaniani, Ragheb & Crainic, Teodor Gabriel & Gendreau, Michel & Rei, Walter, 2017. "The Benders decomposition algorithm: A literature review," European Journal of Operational Research, Elsevier, vol. 259(3), pages 801-817.
    3. Patriksson, Michael, 2008. "A survey on the continuous nonlinear resource allocation problem," European Journal of Operational Research, Elsevier, vol. 185(1), pages 1-46, February.
    4. Xiang Li & Asgeir Tomasgard & Paul I. Barton, 2011. "Nonconvex Generalized Benders Decomposition for Stochastic Separable Mixed-Integer Nonlinear Programs," Journal of Optimization Theory and Applications, Springer, vol. 151(3), pages 425-454, December.
    5. Eduardo Muñoz & Mathias Stolpe, 2011. "Generalized Benders’ Decomposition for topology optimization problems," Journal of Global Optimization, Springer, vol. 51(1), pages 149-183, September.
    6. LOUTE, Etienne, 2003. "Gaussian elimination as a computational paradigm," LIDAM Discussion Papers CORE 2003059, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    7. Walter Rei & Jean-François Cordeau & Michel Gendreau & Patrick Soriano, 2009. "Accelerating Benders Decomposition by Local Branching," INFORMS Journal on Computing, INFORMS, vol. 21(2), pages 333-345, May.
    8. Subramanian, Avinash S.R. & Kannan, Rohit & Holtorf, Flemming & Adams, Thomas A. & Gundersen, Truls & Barton, Paul I., 2023. "Optimization under uncertainty of a hybrid waste tire and natural gas feedstock flexible polygeneration system using a decomposition algorithm," Energy, Elsevier, vol. 284(C).

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