Approximate DouglasRachford algorithm for twosets convex feasibility problems
Abstract
In this paper, we propose a new algorithm combining the DouglasRachford (DR) algorithm and the FrankWolfe algorithm, also known as the conditional gradient (CondG) method, for solving the classic convex feasibility problem. Within the algorithm, which will be named {\it Approximate DouglasRachford (ApDR) algorithm}, the CondG method is used as a subroutine to compute feasible inexact projections on the sets under consideration, and the ApDR iteration is defined based on the DR iteration. The ApDR algorithm generates two sequences, the main sequence, based on the DR iteration, and its corresponding shadow sequence. When the intersection of the feasible sets is nonempty, the main sequence converges to a fixed point of the usual DR operator, and the shadow sequence converges to the solution set. We provide some numerical experiments to illustrate the behaviour of the sequences produced by the proposed algorithm.
 Publication:

arXiv eprints
 Pub Date:
 May 2021
 DOI:
 10.48550/arXiv.2105.13005
 arXiv:
 arXiv:2105.13005
 Bibcode:
 2021arXiv210513005D
 Keywords:

 Mathematics  Optimization and Control;
 65K05;
 90C30;
 90C25