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Analysis Of An Outcome Space Formulation Of The Multiplicative Programming Problem

In: New Frontiers Of Decision Making For The Information Technology Era

Author

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  • H. P. BENSON

    (Department of Decision and Information Sciences, University of Florida, P.O. Box 117169, 351 Stuzin Hall, Gainesville, FL 32611-7169, USA)

  • G. M. BOGER

    (Department of Decision and Information Sciences, University of Florida, P.O. Box 117169, 351 Stuzin Hall, Gainesville, FL 32611-7169, USA)

Abstract

In recent years, researchers and practitioners have become increasingly interested in the multiplicative programming problem. This problem is particularly challenging to solve, since it is a global optimization problem and it is NP-hard. Many of the proposed solution approaches to date for this problem rely on solving an outcome space reformulation of the problem in order to enhance computational efficiency. In this article, we undertake mathematical derivations and analyses of several properties of a common outcome space reformulation of the multiplicative programming problem. The presentation is organized according to whether or not the outcome space reformulation satisfies conditions for the general case, the convex case, or the polyhedral case. Some computational applications of the properties shown in the article are pointed out. Included among these applications is a finite algorithm for finding a strict local optimal solution for the polyhedral case of the outcome space problem.

Suggested Citation

  • H. P. Benson & G. M. Boger, 2000. "Analysis Of An Outcome Space Formulation Of The Multiplicative Programming Problem," World Scientific Book Chapters, in: Yong Shi & Milan Zeleny (ed.), New Frontiers Of Decision Making For The Information Technology Era, chapter 6, pages 100-122, World Scientific Publishing Co. Pte. Ltd..
    • Handle: RePEc:wsi:wschap:9789812792907_0006
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    Cited by:

    1. Harold P. Benson, 2004. "Concave envelopes of monomial functions over rectangles," Naval Research Logistics (NRL), John Wiley & Sons, vol. 51(4), pages 467-476, June.

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