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

@article{DazMilln2021ApproximateDA, title={Approximate Douglas–Rachford algorithm for two-sets convex feasibility problems}, author={R. D{\'i}az Mill{\'a}n and Orizon Pereira Ferreira and Julien Ugon}, journal={Journal of Global Optimization}, year={2021}, pages={1-16} }

In this paper, we propose a new algorithm combining the Douglas–Rachford (DR) algorithm and the Frank–Wolfe algorithm, also known as the conditional gradient (CondG) method, for solving the classic convex feasibility problem. Within the algorithm, which will be named Approximate Douglas–Rachford (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…

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In 1933 von Neumann proved a beautiful result that one can approximate a point in the intersection of two convex sets by alternating projections, i.e., successively projecting on one set and then the…

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