The Douglas-Rachford iteration scheme, introduced half a century ago in connection with nonlinear heat flow problems, aims to find a point common to two or more closed constraint sets. Convergence of the scheme is ensured when the sets are convex subsets of a Hilbert space, however, despite the absence of satisfactory theoretical justification, the scheme has been routinely used to successfully solve a diversity of practical problems in which one or more of the constraints involved is non-convex. As a first step toward addressing this deficiency, we provide convergence results for a prototypical non-convex two-set scenario in which one of the sets is the Euclidean sphere.
CITATION STYLE
Borwein, J. M., & Sims, B. (2011). The douglas-rachford algorithm in the absence of convexity. In Springer Optimization and Its Applications (Vol. 49, pp. 93–109). Springer International Publishing. https://doi.org/10.1007/978-1-4419-9569-8_6
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