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Generalized γ-Valid Cut Procedure for Concave Minimization

Author

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  • H. P. Benson

    (University of Florida)

Abstract

The concept of a γ-valid cutting plane has been used in many types of algorithms for solving concave minimization problems. Unfortunately, the procedures proposed to date for constructing these cuts are valid only under certain assumptions that often may not hold in practice. Chief among these is the requirement that the feasible region of the concave minimization problem in question have full dimension, and that the objective function of this problem be concave rather than quasiconcave. In this article, we propose, validate, and show how to implement a more general γ-valid cutting plane procedure which eliminates these restrictions.

Suggested Citation

  • H. P. Benson, 1999. "Generalized γ-Valid Cut Procedure for Concave Minimization," Journal of Optimization Theory and Applications, Springer, vol. 102(2), pages 289-298, August.
    • Handle: RePEc:spr:joptap:v:102:y:1999:i:2:d:10.1023_a:1021776323080
    DOI: 10.1023/A:1021776323080
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    Cited by:

    1. Marcus Porembski, 2004. "Cutting Planes for Low-Rank-Like Concave Minimization Problems," Operations Research, INFORMS, vol. 52(6), pages 942-953, December.
    2. Darinka Dentcheva & Eli Wolfhagen, 2016. "Two-Stage Optimization Problems with Multivariate Stochastic Order Constraints," Mathematics of Operations Research, INFORMS, vol. 41(1), pages 1-22, February.

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