From Parallel to Sequential Projection Methods and Vice Versa in Convex Feasibility: Results and Conjectures

We present in this article a brief account on the relationship between parallel and sequential projection methods for solving the convex feasibility problem. It is known that fully parallel methods ‘solve’ the problem in the infeasible case, computing a least squares solution, whenever it exists. We are mainly concerned with the fact that this property can be extended to sequential, or block parallel methods, using a suitable underrelaxation. We show that classical results on nonexpansive mappings could be used to, prove some of these properties and we present several conjectures and new results.

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