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Algoritmy pro vybrané geometrické problémy nad zonotopy a jejich aplikace v optimalizaci a v analýze dat / Algorithms for various geometric problems over zonotopes and their applications in optimization and data analysis

The thesis unifies the most important author's results in the field of algorithms concerning zonotopes and their applications in optimization and statistics. The computational-geometric results consist of a new compact output-sensitive algorithm for enumerating vertices of a zonotope, which outperforms the rival algorithm with the same complexity-theoretic properties both theoretically and empirically, and a polynomial algorithm for arbitrarily precise approximation of a zonotope with the Löwner-John ellipsoid. In the application area, the thesis presents a result, which connects linear regression model with interval outputs with the zonotope matters. The usage of presented geometric algorithms for solving a nonconvex optimisation problem is also discussed.

Identiferoai:union.ndltd.org:nusl.cz/oai:invenio.nusl.cz:199386
Date January 2009
CreatorsRada, Miroslav
ContributorsČerný, Michal, Vlach, Milan, Kopa, Miloš
PublisherVysoká škola ekonomická v Praze
Source SetsCzech ETDs
LanguageCzech
Detected LanguageEnglish
Typeinfo:eu-repo/semantics/doctoralThesis
Rightsinfo:eu-repo/semantics/restrictedAccess

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