Journal of Convex Analysis 24 (2017), No. 2, 477--492
Copyright Heldermann Verlag 2017
Computations of Quasiconvex Hulls of Isotropic Sets
Sebastian Heinz
Weierstraß-Institut für Analysis und Stochastik, Mohrenstr. 39, 10117 Berlin, Germany
heinz@wias-berlin.de
Martin Kruzík
Institute of Information Theory and Automation, Academy of Sciences, Pod vodárenskou vezí 4, 182 08 Praha 8, Czech Republic
kruzik@utia.cas.cz
We design an algorithm for computations of quasiconvex hulls of isotropic compact sets in in the space of 2×2 real matrices. Our approach uses a recent result by the first author [Adv. Calc. Var. 8 (2015) 43--53] on quasiconvex hulls of isotropic compact sets in the space of 2×2 real matrices. We show that our algorithm has the time complexity of O(N log N) where N is the number of orbits of the set. Finally, we outline some applications of our results to relaxation of L∞ variational problems.
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