Miroslav Rada, Elif Garajová, Jaroslav Horáček, and Milan Hladík. A new pruning test for parametric interval linear systems. In Proceedings of the 15th International Symposium on Operational Research SOR'19, Bled, Slovenia, September 25-27, 2019, pp. 506–511, Slovenian Society Informatika, Ljubljana, Slovenia, 2019.
We deal with the weak solution set of parametric interval linear systems. We adopt the branch-and-prune SIVIA algorithm to obtain an outer approximation of the weak solution set and, if possible, also an inner approximation. We propose a new pruning test, based on the fact that solvability of a linear system can be viewed as a zonotope membership problem. The proposed test works efficiently in its full strength especially when pruning infeasible boxes.
@inProceedings{RadGar2019a,
author = "Miroslav Rada and Elif Garajov\'{a} and Jaroslav Hor\'{a}{\v{c}}ek and Milan Hlad\'{\i}k",
title = "A new pruning test for parametric interval linear systems",
editor = "L. Zadnik Stirn and others",
booktitle = "Proceedings of the 15th International Symposium on Operational Research SOR'19, Bled, Slovenia, September 25-27, 2019",
publisher = "Slovenian Society Informatika",
address = "Ljubljana, Slovenia",
pages = "506-511",
year = "2019",
isbn = "978-961-6165-55-6",
bib2html_dl_pdf = "http://fgg-web.fgg.uni-lj.si/~/sdrobne/sor/SOR'19%20-%20Proceedings.pdf",
abstract = "We deal with the weak solution set of parametric interval linear systems. We adopt the branch-and-prune SIVIA algorithm to obtain an outer approximation of the weak solution set and, if possible, also an inner approximation. We propose a new pruning test, based on the fact that solvability of a linear system can be viewed as a zonotope membership problem. The proposed test works efficiently in its full strength especially when pruning infeasible boxes.",
keywords = "Parametric interval linear systems; Branch-and-prune; Zonotope",
}
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