Minimization of Isotonic Functions Composed of Fractions

J. Y. Lin, S. Schaible, Ruey-Lin Sheu

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Abstract

In this paper, we introduce a class of minimization problems whose objective function is the composite of an isotonic function and finitely many ratios. Examples of an isotonic function include the max-operator, summation, and many others, so it implies a much wider class than the classical fractional programming containing the minimax fractional program as well as the sum-of-ratios problem. Our intention is to develop a generic "Dinkelbach-like" algorithm suitable for all fractional programs of this type. Such an attempt has never been successful before, including an early effort for the sum-of-ratios problem. The difficulty is now overcome by extending the cutting plane method of Barros and Frenk (in J. Optim. Theory Appl. 87:103-120, 1995). Based on different isotonic operators, various cuts can be created respectively to either render a Dinkelbach-like approach for the sum-of-ratios problem or recover the classical Dinkelbach-type algorithm for the min-max fractional programming.

Original languageEnglish
Pages (from-to)581-601
Number of pages21
JournalJournal of Optimization Theory and Applications
Volume146
Issue number3
DOIs
Publication statusPublished - 2010 May 6

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All Science Journal Classification (ASJC) codes

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

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