The Maximax Minimax Quotient Theorem

Jean Baptiste Bouvier, Melkior Ornik

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)1084-1101
Number of pages18
JournalJournal of Optimization Theory and Applications
Issue number3
StatePublished - Mar 2022


  • Fractional programming
  • Max-min programming
  • Optimization
  • Polytopes

ASJC Scopus subject areas

  • Control and Optimization
  • Applied Mathematics
  • Management Science and Operations Research


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