Minimization of Isotonic Functions Composed of Fractions

Autor: S. Schaible, Jen-Yen Lin, Ruey-Lin Sheu
Rok vydání: 2010
Předmět:
Zdroj: Journal of Optimization Theory and Applications. 146:581-601
ISSN: 1573-2878
0022-3239
DOI: 10.1007/s10957-010-9684-3
Popis: 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.
Databáze: OpenAIRE
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