Approximate Douglas–Rachford algorithm for two-sets convex feasibility problems

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