The fun is finite: Douglas-Rachford and Sudoku puzzle – Finite termination and local linear convergence

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