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A Branch-and-Bound Method for Reversed Geometric Programming

Author

Listed:
  • Willy Gochet

    (CORE, Louvain-La Neuve, Belgium)

  • Yves Smeers

    (CORE, Louvain-La Neuve, Belgium)

Abstract

A general or signomial geometric program is a nonlinear mathematical program involving general polynomials in several variables both in the objective function and the constraints. A branch-and-bound method is proposed for this extensive class of nonconvex optimization programs guaranteeing convergence to the global optimum. The subproblems to be solved are convex but the method can easily be combined with a cutting plane technique to generate subproblems which are linear. A simple example is given to illustrate the technique. The combined method involving linear subproblems has been coded and numerical experience with this code will be reported later.

Suggested Citation

  • Willy Gochet & Yves Smeers, 1979. "A Branch-and-Bound Method for Reversed Geometric Programming," Operations Research, INFORMS, vol. 27(5), pages 982-996, October.
    • Handle: RePEc:inm:oropre:v:27:y:1979:i:5:p:982-996
    DOI: 10.1287/opre.27.5.982
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    Cited by:

    1. Hansen, Jared M. & Raut, Sumit & Swami, Sanjeev, 2010. "Retail Shelf Allocation: A Comparative Analysis of Heuristic and Meta-Heuristic Approaches," Journal of Retailing, Elsevier, vol. 86(1), pages 94-105.
    2. Yang, Ming-Hsien & Chen, Wen-Cher, 1999. "A study on shelf space allocation and management," International Journal of Production Economics, Elsevier, vol. 60(1), pages 309-317, April.
    3. Murray, Chase C. & Talukdar, Debabrata & Gosavi, Abhijit, 2010. "Joint Optimization of Product Price, Display Orientation and Shelf-Space Allocation in Retail Category Management," Journal of Retailing, Elsevier, vol. 86(2), pages 125-136.
    4. Hasmukh Gajjar & Gajendra Adil, 2010. "A piecewise linearization for retail shelf space allocation problem and a local search heuristic," Annals of Operations Research, Springer, vol. 179(1), pages 149-167, September.
    5. Yang, Ming-Hsien, 2001. "An efficient algorithm to allocate shelf space," European Journal of Operational Research, Elsevier, vol. 131(1), pages 107-118, May.
    6. S Raut & S Swami & M P Moholkar, 2009. "Heuristic and meta-heuristic approaches for multi-period shelf-space optimization: the case of motion picture retailing," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(10), pages 1335-1348, October.

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