On the finite convergence of the Douglas-Rachford algorithm for solving (not necessarily convex) feasibility problems in Euclidean spaces
arXiv:1604.0465726 citationsh-index: 50
Originality Incremental advance
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Provides theoretical guarantees for finite convergence of a widely used algorithm, benefiting researchers and practitioners in optimization and applied mathematics.
The paper identifies new conditions under which the Douglas-Rachford algorithm converges in finitely many steps for solving feasibility problems, including nonconvex cases, and illustrates these with examples.
Solving feasibility problems is a central task in mathematics and the applied sciences. One particularly successful method is the Douglas-Rachford algorithm. In this paper, we provide many new conditions sufficient for finite convergence. Numerous examples illustrate our results.