Finding a best approximation pair of points for two polyhedra

Ron Aharoni, Yair Censor, Zilin Jiang
2018 Computational optimization and applications  
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
more » ... egotiable than projections on the polyhedra themselves. A central component in the proposed process is the Halpern--Lions--Wittmann--Bauschke algorithm for approaching the projection of a given point onto a convex set.
doi:10.1007/s10589-018-0021-3 fatcat:dqpv4qttijeuzfweflp2nao7eq