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A note on the finite convergence of alternating projections

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Open access
Authors
Bui, Hoa
Loxton, Ryan
Moeini, A.
Date
2021
Type
Journal Article

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Bui, H.T. and Loxton, R. and Moeini, A. 2021. A note on the finite convergence of alternating projections. Operations Research Letters. 49 (3): pp. 431-438.
Source Title
Operations Research Letters
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Faculty
Faculty of Science and Engineering
School
School of Elec Eng, Comp and Math Sci (EECMS)
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Abstract

We establish sufficient conditions for finite convergence of the alternating projections method for two non-intersecting and potentially nonconvex sets. Our results are based on a generalization of the concept of intrinsic transversality, which until now has been restricted to sets with nonempty intersection. In the special case of a polyhedron and closed half space, our sufficient conditions define the minimum distance between the two sets that is required for alternating projections to converge in a single iteration.