Milan Hladík. Generalized linear fractional programming under interval uncertainty. Eur. J. Oper. Res., 205(1):42–46, 2010.
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Data in many real-life engineering and economical problems suffer from inexactness. Herein we assume that we are given some intervals in which the data can simultaneously and independently perturb. We consider a generalized linear fractional programming problem with interval data and present an efficient method for computing the range of optimal values. The method reduces the problem to solving from two to four real-valued generalized linear fractional programs, which can be computed in polynomial time using an appropriate interior point method solver. We consider also the inverse problem: How much can data of a real generalized linear fractional program vary such that the optimal values do not exceed some prescribed bounds. We propose a method for calculating (often the largest possible) ranges of admissible variations; it needs to solve only two real-valued generalized linear fractional programs. We illustrate the approach on a simple von Neumann economic growth model.
@article{Hla2010c,
author = "Milan Hlad\'{\i}k",
title = "Generalized linear fractional programming under interval uncertainty",
journal = "Eur. J. Oper. Res.",
fjournal = "European Journal of Operational Research",
volume = "205",
number = "1",
pages = "42-46",
year = "2010",
doi = "10.1016/j.ejor.2010.01.018",
bib2html_dl_html = "http://dx.doi.org/10.1016/j.ejor.2010.01.018",
abstract = "Data in many real-life engineering and economical problems suffer from inexactness. Herein we assume that we are given some intervals in which the data can simultaneously and independently perturb. We consider a generalized linear fractional programming problem with interval data and present an efficient method for computing the range of optimal values. The method reduces the problem to solving from two to four real-valued generalized linear fractional programs, which can be computed in polynomial time using an appropriate interior point method solver.
We consider also the inverse problem: How much can data of a real generalized linear fractional program vary such that the optimal values do not exceed some prescribed bounds. We propose a method for calculating (often the largest possible) ranges of admissible variations; it needs to solve only two real-valued generalized linear fractional programs. We illustrate the approach on a simple von Neumann economic growth model.",
keywords = "generalized linear fractional programming, interval analysis, tolerance analysis, sensitivity analysis, economic growth model",
}
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