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Complexity of Methods for Approximating Convex Compact Bodies by Double Description Polytopes and Complexity Bounds for a Hyperball

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Abstract

A comparative analysis of the complexity of approaches to the approximation of convex compact bodies by double description polytopes is provided as applied to a ball. A complexity bound for the Estimate Refinement method is obtained in the case of approximation of a multidimensional ball.

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ACKNOWLEDGMENTS

The author is sincerely grateful to G.K. Kamenev for his interest in this work, valuable comments, and discussion of the results.

Funding

This work was supported in part by the Spanish National Research Council (CSIC) (MTM2017-86875-C3-1-R).

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Authors and Affiliations

  1. Universidad Rey Juan Carlos, 28933, Móstoles, Madrid, Spain

    R. V. Efremov

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Translated by I. Ruzanova

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Efremov, R.V. Complexity of Methods for Approximating Convex Compact Bodies by Double Description Polytopes and Complexity Bounds for a Hyperball. Comput. Math. and Math. Phys. 59, 1204–1213 (2019). https://doi.org/10.1134/S0965542519070066

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