Aragón Artacho, Francisco Javier, Borwein, Jonathan M., Tam, Matthew K.
Global behavior of the Douglas–Rachford method for a nonconvex feasibility problem
Journal of Global Optimization. 2016, 65(2): 309-327. doi:10.1007/s10898-015-0380-6
URI: http://hdl.handle.net/10045/55937
DOI: 10.1007/s10898-015-0380-6
ISSN: 0925-5001 (Print)
Abstract: 
In recent times the Douglas–Rachford algorithm has been observed empirically to solve a variety of nonconvex feasibility problems including those of a combinatorial nature. For many of these problems current theory is not sufficient to explain this observed success and is mainly concerned with questions of local convergence. In this paper we analyze global behavior of the method for finding a point in the intersection of a half-space and a potentially non-convex set which is assumed to satisfy a well-quasi-ordering property or a property weaker than compactness. In particular, the special case in which the second set is finite is covered by our framework and provides a prototypical setting for combinatorial optimization problems.
Keywords:Douglas–Rachford algorithm, Global convergence, Feasibility problem, Half-space, Non-convex
Springer Science+Business Media New York
info:eu-repo/semantics/article