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In recent years, the Douglas-Rachford splitting method has been shown to beeffective at solving many non-convex optimization problems. In this paper wepresent a local convergence analysis for non-convex feasibility problems andshow that both finite termination and local linear convergence are obtained.For a generalization of the Sudoku puzzle, we prove that the local linear rateof convergence of Douglas-Rachford is exactly $\frac{\sqrt{5}}{5}$ andindependent of puzzle size. For the $s$-queens problem we prove thatDouglas-Rachford converges after a finite number of iterations. Numericalresults on solving Sudoku puzzles and $s$-queens puzzles are provided tosupport our theoretical findings.

The Fun is Finite: Douglas-Rachford and Sudoku Puzzle -- Finite Termination and Local Linear Convergence