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Variations on a cutting plane method for solving concave minimization problems with linear constraints

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  • A. Victor Cabot

Abstract

A cutting plane method for solving concave minimization problems with linear constraints has been advanced by Tui. The principle behind this cutting plane has been applied to integer programming by Balas, Young, Glover, and others under the name of convexity cuts. This paper relates the question of finiteness of Tui's method to the so‐called generalized lattice point problem of mathematical programming and gives a sufficient condition for terminating Tui's method. The paper then presents several branch‐and‐bound algorithms for solving concave minimization problems with linear constraints with the Tui cut as the basis for the algorithm. Finally, some computational experience is reported for the fixed‐charge transportation problem.

Suggested Citation

  • A. Victor Cabot, 1974. "Variations on a cutting plane method for solving concave minimization problems with linear constraints," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 21(2), pages 265-274, June.
    • Handle: RePEc:wly:navlog:v:21:y:1974:i:2:p:265-274
    DOI: 10.1002/nav.3800210206
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    Cited by:

    1. Kurt M. Bretthauer, 1994. "A penalty for concave minimization derived from the tuy cutting plane," Naval Research Logistics (NRL), John Wiley & Sons, vol. 41(3), pages 455-463, April.
    2. Harold P. Benson, 1996. "Deterministic algorithms for constrained concave minimization: A unified critical survey," Naval Research Logistics (NRL), John Wiley & Sons, vol. 43(6), pages 765-795, September.
    3. Reiner Horst, 1990. "Deterministic methods in constrained global optimization: Some recent advances and new fields of application," Naval Research Logistics (NRL), John Wiley & Sons, vol. 37(4), pages 433-471, August.
    4. Kurt M. Bretthauer & A. Victor Cabot & M. A. Venkataramanan, 1994. "An algorithm and new penalties for concave integer minimization over a polyhedron," Naval Research Logistics (NRL), John Wiley & Sons, vol. 41(3), pages 435-454, April.

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