# Finding a best approximation pair of points for two polyhedra

@article{Aharoni2018FindingAB, title={Finding a best approximation pair of points for two polyhedra}, author={Ron Aharoni and Yair Censor and Zilin Jiang}, journal={Computational Optimization and Applications}, year={2018}, volume={71}, pages={509-523} }

Given two disjoint convex polyhedra, we look for a best approximation pair relative to them, i.e., a pair of points, one in each polyhedron, attaining the minimum distance between the sets. Cheney and Goldstein showed that alternating projections onto the two sets, starting from an arbitrary point, generate a sequence whose two interlaced subsequences converge to a best approximation pair. We propose a process based on projections onto the half-spaces defining the two polyhedra, which are more…

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Alternative algorithms that utilize projection and proximity operators are presented that are competitive and sometimes superior to the one proposed by Aharoni et al.

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