Shadow DouglasRachford Splitting for Monotone Inclusions
Abstract
In this work, we propose a new algorithm for finding a zero in the sum of two monotone operators where one is assumed to be singlevalued and Lipschitz continuous. This algorithm naturally arises from a nonstandard discretization of a continuous dynamical system associated with the DouglasRachford splitting algorithm. More precisely, it is obtained by performing an explicit, rather than implicit, discretization with respect to one of the operators involved. Each iteration of the proposed algorithm requires the evaluation of one forward and one backward operator.
 Publication:

arXiv eprints
 Pub Date:
 March 2019
 arXiv:
 arXiv:1903.03393
 Bibcode:
 2019arXiv190303393C
 Keywords:

 Mathematics  Optimization and Control;
 49M29;
 90C25;
 47H05;
 47J20;
 65K15
 EPrint:
 Applied Mathematics &