The Douglas-Rachford algorithm converges weakly to a normal solution of minimizing a convex function over a linear subspace even when the original problem is infeasible.
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On the behaviour of the Douglas-Rachford algorithm for minimizing a convex function subject to a linear constraint
The Douglas-Rachford algorithm converges weakly to a normal solution of minimizing a convex function over a linear subspace even when the original problem is infeasible.