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Solving a Class of Multiplicative Programs with 0–1 Knapsack Constraints

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  • T. Kuno

    (University of Tsukuba)

Abstract

We develop a branch-and-bound algorithm to solve a nonlinear class of 0–1 knapsack problems. The objective function is a product of m≥2 affine functions, whose variables are mutually exclusive. The branching procedure in the proposed algorithm is the usual one, but the bounding procedure exploits the special structure of the problem and is implemented through two stages: the first stage is based on linear programming relaxation; the second stage is based on Lagrangian relaxation. Computational results indicate that the algorithm is promising.

Suggested Citation

  • T. Kuno, 1999. "Solving a Class of Multiplicative Programs with 0–1 Knapsack Constraints," Journal of Optimization Theory and Applications, Springer, vol. 103(1), pages 121-135, October.
    • Handle: RePEc:spr:joptap:v:103:y:1999:i:1:d:10.1023_a:1021725517203
    DOI: 10.1023/A:1021725517203
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    References listed on IDEAS

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    1. Arthur M. Geoffrion, 1967. "Solving Bicriterion Mathematical Programs," Operations Research, INFORMS, vol. 15(1), pages 39-54, February.
    2. James E. Falk & Richard M. Soland, 1969. "An Algorithm for Separable Nonconvex Programming Problems," Management Science, INFORMS, vol. 15(9), pages 550-569, May.
    3. Egon Balas & Eitan Zemel, 1980. "An Algorithm for Large Zero-One Knapsack Problems," Operations Research, INFORMS, vol. 28(5), pages 1130-1154, October.
    4. 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.
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