Michal Černý and Milan Hladík. Optimization with uncertain, inexact or unstable data: Linear programming and the interval approach. In Proceedings of the 10th International Conference on Strategic Management and its Support by Information Systems, pp. 35–43, VŠB - Technical University of Ostrava, Ostrava, 2013.
This paper accompanies our invited lecture on interval methods in optimization. First, we put the interval approach in context with other approaches to modeling inexactness, instability or imprecision of input data; in particular, we discuss the stochastic and fuzzy approach. Then we turn to interval linear programming. We show some important aspects in which the interval-valued linear programs differ from traditional linear programs. We emphasize how various formulations of the auxiliary linear program, which are equivalent in the traditional setting, differ in the interval setting from the computational point of view. We also consider some natural questions, e.g. weak and strong feasibility and the problem of finding the range of possible optimal values and the catastrophic scenario. We also point out some (subjectively selected) interesting open problems in the field.
@inProceedings{CerHla2013a,
author = "Michal {\v{C}}ern\'{y} and Milan Hlad\'{\i}k",
editor = "Radek N\v{e}mec and Franti\v{s}ek Zapletal",
title = "Optimization with uncertain, inexact or unstable data: Linear programming and the interval approach",
booktitle = "Proceedings of the 10th International Conference on Strategic Management and its Support by Information Systems",
publisher = "V\v{S}B - Technical University of Ostrava",
address = "Ostrava",
pages = "35-43",
year = "2013",
isbn = "978-80-248-3096-4",
bib2html_dl_pdf = "https://kam.mff.cuni.cz/~hladik/doc/2013-proc-SMSIS-OptUncDataIntAppr.pdf",
abstract = "This paper accompanies our invited lecture on interval methods in optimization. First, we put the interval approach in context with other approaches to modeling inexactness, instability or imprecision of input data; in particular, we discuss the stochastic and fuzzy approach. Then we turn to interval linear programming. We show some important aspects in which the interval-valued linear programs differ from traditional linear programs. We emphasize how various formulations of the auxiliary linear program, which are equivalent in the traditional setting, differ in the interval setting from the computational point of view. We also consider some natural questions, e.g. weak and strong feasibility and the problem of finding the range of possible optimal values and the catastrophic scenario. We also point out some (subjectively selected) interesting open problems in the field.",
keywords = "Interval optimization, Interval linear programming,
Inexact data, Interval data, Open problems",
}
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