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Zh. Vychisl. Mat. Mat. Fiz., 2009, Volume 49, Number 9, Pages 1571–1578 (Mi zvmmf4749)  

A criterion for checking if a convex set belongs to the union of a finite number of convex sets

D. G. Pivovarchuk

Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow, 119992, Russia

Abstract: A necessary and sufficient condition for the inclusion of a convex compact set in the union of a finite number of convex sets is proved. This condition obtained using the convex analysis techniques is a condition on the maximin of a given function. Using the dynamic programming, checking this condition is reduced to evaluating a set of functions and checking a condition for their values. The reduced form of the criterion is more convenient from the computational point of view.

Key words: convex sets, union of sets, convex analysis, dynamic programming, optimal control.

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English version:
Computational Mathematics and Mathematical Physics, 2009, 49:9, 1499–1506

Bibliographic databases:

UDC: 519.658
Received: 08.12.2008

Citation: D. G. Pivovarchuk, “A criterion for checking if a convex set belongs to the union of a finite number of convex sets”, Zh. Vychisl. Mat. Mat. Fiz., 49:9 (2009), 1571–1578; Comput. Math. Math. Phys., 49:9 (2009), 1499–1506

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  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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