Gearhart-Koshy acceleration for affine subspaces
Matthew K Tam
OPERATIONS RESEARCH LETTERS | ELSEVIER | Published : 2021
The method of cyclic projections finds nearest points in the intersection of finitely many affine subspaces. To accelerate convergence, Gearhart & Koshy proposed a modification which, in each iteration, performs an exact line search based on minimising the distance to the solution. When the subspaces are linear, the procedure can be made explicit using feasibility of the zero vector. This work studies an alternative approach which does not rely on this fact, thus providing an efficient implementation in the affine setting.
Awarded by Australian Research Council
This work is supported in part by DE200100063 from the Australian Research Council. The author would like to thank Janosch Rieger for discussions relating to  which initiated this work, and the anonymous referee and editor for their helpful comments and suggestions.