Abstract: The Douglas–Rachford algorithm is a very popular splitting technique for finding a zero of the sum of two maximally monotone operators. The behaviour of the algorithm remains mysterious in the general inconsis-tent case, i.e., when the sum problem has no zeros. However, more than a decade ago, it was shown that in the (possibly inconsistent) convex feasibility setting, the shadow sequence remains bounded and its weak cluster points solve a best approximation problem. In this talk, we advance the understanding of the inconsistent case significantly by presenting a complete proof of the full weak convergence in the convex feasibility setting. We also provide linear rate of convergence and strong convergence in special cases.
The Douglas-Rachford method for solving possibly inconsistent sum problems
15.12.2016 15:15 - 16:15
Organiser:
RI Bot, A. Neumaier, H. Schichl
Location: