Line Search for Averaged Operator Iteration

P. Giselsson, M. Fält, and S. Boyd

Proceedings IEEE Conference on Decision and Control, pages 1015-1022, December 2016.

Many popular first order algorithms for convex optimization, such as forward-backward splitting, Douglas-Rachford splitting, and the alternating direction method of multipliers (ADMM), can be formulated as averaged iteration of a nonexpansive mapping. In this paper we propose a line search for averaged iteration that preserves the theoretical convergence guarantee, while often accelerating practical convergence. We discuss several general cases in which the additional computational cost of the line search is modest compared to the savings obtained.