The Maximax Minimax Quotient Theorem

Jean-Baptiste Bouvier () and Melkior Ornik ()
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Jean-Baptiste Bouvier: University of Illinois at Urbana-Champaign
Melkior Ornik: University of Illinois at Urbana-Champaign

Journal of Optimization Theory and Applications, 2022, vol. 192, issue 3, No 14, 1084-1101

Abstract: 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.

Keywords: Optimization; Fractional programming; Max-min programming; Polytopes; 49K35; 90C32; 90C47 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10957-022-02008-z

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