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Concave Minimization Via Collapsing Polytopes

Author

Listed:
  • James E. Falk

    (The George Washington University, Washington, D.C.)

  • Karla L. Hoffman

    (National Bureau of Standards, Gaithersburg, Maryland)

Abstract

We present a procedure for globally minimizing a concave function over a (bounded) polytope by successively minimizing the function over polytopes containing the feasible region, and collapsing to the feasible region. The initial containing polytope is a simplex, and, at the k th iteration, the procedure chooses the most promising vertex of the current containing polytope to refine the approximation. The method generates a tree whose ultimate terminal nodes coincide with the vertices of the feasible region, and accounts for the vertices of the containing polytopes.

Suggested Citation

  • James E. Falk & Karla L. Hoffman, 1986. "Concave Minimization Via Collapsing Polytopes," Operations Research, INFORMS, vol. 34(6), pages 919-929, December.
    • Handle: RePEc:inm:oropre:v:34:y:1986:i:6:p:919-929
    DOI: 10.1287/opre.34.6.919
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    Cited by:

    1. Matthew E. Wilhelm & Matthew D. Stuber, 2023. "Improved Convex and Concave Relaxations of Composite Bilinear Forms," Journal of Optimization Theory and Applications, Springer, vol. 197(1), pages 174-204, 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. Pey-Chun Chen & Pierre Hansen & Brigitte Jaumard & Hoang Tuy, 1998. "Solution of the Multisource Weber and Conditional Weber Problems by D.-C. Programming," Operations Research, INFORMS, vol. 46(4), pages 548-562, August.

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