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A Simplicial Branch and Bound Duality‐Bounds Algorithm to Linear Multiplicative Programming

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  • Xue-Gang Zhou
  • Bing-Yuan Cao

Abstract

A simplicial branch and bound duality‐bounds algorithm is presented to globally solving the linear multiplicative programming (LMP). We firstly convert the problem (LMP) into an equivalent programming one by introducing p auxiliary variables. During the branch and bound search, the required lower bounds are computed by solving ordinary linear programming problems derived by using a Lagrangian duality theory. The proposed algorithm proves that it is convergent to a global minimum through the solutions to a series of linear programming problems. Some examples are given to illustrate the feasibility of the present algorithm.

Suggested Citation

  • Xue-Gang Zhou & Bing-Yuan Cao, 2013. "A Simplicial Branch and Bound Duality‐Bounds Algorithm to Linear Multiplicative Programming," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnljam:v:2013:y:2013:i:1:n:984168
    DOI: 10.1155/2013/984168
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    References listed on IDEAS

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    1. M. Raghavachari, 1969. "On Connections Between Zero-One Integer Programming and Concave Programming Under Linear Constraints," Operations Research, INFORMS, vol. 17(4), pages 680-684, August.
    2. H. P. Benson & G. M. Boger, 1997. "Multiplicative Programming Problems: Analysis and Efficient Point Search Heuristic," Journal of Optimization Theory and Applications, Springer, vol. 94(2), pages 487-510, August.
    3. John M. Mulvey & Robert J. Vanderbei & Stavros A. Zenios, 1995. "Robust Optimization of Large-Scale Systems," Operations Research, INFORMS, vol. 43(2), pages 264-281, April.
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