Minimization of Isotonic Functions Composed of Fractions

J.-Y. Lin, S. Schaible () and R.-L. Sheu
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J.-Y. Lin: National Chiayi University
S. Schaible: Chung Yuan Christian University
R.-L. Sheu: National Cheng Kung University

Journal of Optimization Theory and Applications, 2010, vol. 146, issue 3, No 3, 601 pages

Abstract: 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.

Keywords: Sum-of-ratios problem; Min-max fractional programming; Isotonic function; Dinkelbach-type algorithm; Cutting plane method (search for similar items in EconPapers)
Date: 2010
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DOI: 10.1007/s10957-010-9684-3

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