On the Convex Feasibility Problem

Details On the Convex Feasibility Problem On the Convex Feasibility Problem

2009-05-29

arxiv.org/abs/0905.4909v1

Ann. Univ. Tibiscus Comp. Sci. Series VII(2009),225-238

Computer Science

Numerical Analysis

14 pages, exposed on 5th International Conference "Actualities and Perspectives on Hardware and Software" - APHS2009, Timisoar

Scientific paper

The convergence of the projection algorithm for solving the convex feasibility problem for a family of closed convex sets, is in connection with the regularity properties of the family. In the paper [18] are pointed out four cases of such a family depending of the two characteristics: the emptiness and boudedness of the intersection of the family. The case four (the interior of the intersection is empty and the intersection itself is bounded) is unsolved. In this paper we give a (partial) answer for the case four: in the case of two closed convex sets in R3 the regularity property holds.

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