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On the Douglas–Rachford Algorithm for Solving Possibly Inconsistent Optimization Problems

On the Douglas–Rachford Algorithm for Solving Possibly Inconsistent Optimization Problems

More than 40 years ago, Lions and Mercier introduced in a seminal paper the Douglas–Rachford algorithm. Today, this method is well-recognized as a classic and highly successful splitting method to find minimizers of the sum of two (not necessarily smooth) convex functions. Whereas the underlying theory has matured, one case …