A Lyapunov function construction for the Douglas-Rachford operator in a non-convex setting

Ohad Giladi, Björn S. Rüffer

Published 2017-08-29Version 1

Local quadratic Lyapunov functions are combined to a global Lyapunov function for the Douglas-Rachford algorithm in the case of a non-convex geometry, in order to prove global convergence to the intersection points, as well as various robustness properties. Specifically, the case where one set is a line and the other a union of two lines is considered, with the latter set being non-convex. An explicit formula for the global Lyapunov function is given in terms of the problem parameters.