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The Maximax Minimax Quotient Theorem

Author

Listed:
  • Jean-Baptiste Bouvier

    (University of Illinois at Urbana-Champaign)

  • Melkior Ornik

    (University of Illinois at Urbana-Champaign)

Abstract

We present an optimization problem emerging from optimal control theory and situated at the intersection of fractional programming and linear max-min programming on polytopes. A naïve solution would require solving four nested, possibly nonlinear, optimization problems. Instead, relying on numerous geometric arguments we determine an analytical solution to this problem. In the course of proving our main theorem, we also establish another optimization result stating that the minimum of a specific minimax optimization is located at a vertex of the constraint set.

Suggested Citation

  • Jean-Baptiste Bouvier & Melkior Ornik, 2022. "The Maximax Minimax Quotient Theorem," Journal of Optimization Theory and Applications, Springer, vol. 192(3), pages 1084-1101, March.
    • Handle: RePEc:spr:joptap:v:192:y:2022:i:3:d:10.1007_s10957-022-02008-z
    DOI: 10.1007/s10957-022-02008-z
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    References listed on IDEAS

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    1. Charalambos D. Aliprantis & Kim C. Border, 2006. "Infinite Dimensional Analysis," Springer Books, Springer, edition 0, number 978-3-540-29587-7, September.
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