Milan Hladík. An interval linear programming contractor. In Proceedings 30th International Conference on Mathematical Methods in Economics 2012, Karviná, Czech Republic, pp. 284–289 (Part I.), Silesian University in Opava, School of Business Administration in Karviná, September 2012.
We consider linear programming with interval data. One of the most challenging problems in this topic is to determine or tight approximate the set of all optimal solutions subject to all perturbations within the given intervals. We propose an iterative method that finds an enclosure of the set of optimal solutions. The method is based on a linear approximation and sequential refinement. It runs in polynomial time, so, naturally, convergence to the ideal set cannot be ensured. We apply the method in a simple portfolio selection problem with uncertain data.
@InProceedings{Hla2012c,
author = "Milan Hlad\'{\i}k",
editor = "Jaroslav Ram{\'\i}k and Daniel Stav\'{a}rek",
title = "An interval linear programming contractor",
booktitle = "Proceedings 30th International Conference on Mathematical Methods in Economics 2012, Karvin\'{a}, Czech Republic",
year = "2012",
pages = "284-289 (Part I.)",
month = "September",
publisher = "Silesian University in Opava, School of Business Administration in Karvin\'{a}",
isbn = "978-80-7248-779-0",
bib2html_dl_pdf = "https://kam.mff.cuni.cz/~hladik/doc/2012-conf-MME-ILPcontr.pdf",
abstract = "We consider linear programming with interval data. One of the most challenging problems in this topic is to determine or tight approximate the set of all optimal solutions subject to all perturbations within the given intervals. We propose an iterative method that finds an enclosure of the set of optimal solutions. The method is based on a linear approximation and sequential refinement. It runs in polynomial time, so, naturally, convergence to the ideal set cannot be ensured. We apply the method in a simple portfolio selection problem with uncertain data.",
keywords = "interval linear programming, interval analysis, portfolio selection",
}
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