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The initial convergence rate of adaptive methods for polyhedral approximation of convex bodies. (Russian, English) Zbl 1164.90424

Zh. Vychisl. Mat. Mat. Fiz. 48, No. 5, 763-778 (2008); translation in Comput. Math. Math. Phys. 48, No. 5, 724-738 (2008).
Summary: The convergence rate at the initial stage is analyzed for a previously proposed class of asymptotically optimal adaptive methods for polyhedral approximation of convex bodies. Based on the results, the initial convergence rate of these methods can be evaluated for arbitrary bodies (including the case of polyhedral approximation of polytopes) and the resources sufficient for achieving optimal asymptotic properties can be estimated.

MSC:

90C57 Polyhedral combinatorics, branch-and-bound, branch-and-cut
90C59 Approximation methods and heuristics in mathematical programming
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