Finding a best approximation pair of points for two polyhedra

Published: 2017/08/02

Convex Optimization, Polyhedra alternating projection methods, best approximation pair, convex polyhedra, half-spaces Short URL: https://optimization-online.org/?p=17351

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 negotiable 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.

Finding a best approximation pair of points for two polyhedra

Citation

Article