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←Created page with ''''Projections onto Convex Sets''' (POCS), sometimes known as the '''alternating projection''' method, is a method to find a point in the intersection of two [[c...' |
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Unlike [[Dykstra's projection algorithm]], the solution need not be a projection onto the intersection ''C'' and ''D''.
== Related algorithms ==
The method of '''averaged projections''' is quite similar. For the case of two closed convex sets ''C'' and ''D'', it proceeds by
<math> x_{k+1} = \frac{1}{2}( \mathcal{P}_C(x_k) + \mathcal{P}_D(x_k) ) </math>
It has long been known to converge globally.<ref> A. Auslender. Methodes Numeriques pour la Resolution des Problems
d’Optimisation avec Constraintes. PhD thesis, Faculte des Sciences, Grenoble, 1969</ref>. Furthermore, the method is easy to generalize to more than two sets; some convergence results for this case are in <ref>Local convergence for alternating and averaged nonconvex projections. A Lewis, R Luke, J Malick, 2007. [http://arxiv.org/abs/0709.0109 arXiv]</ref>.
== References ==
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