Details

Autor(en) / Beteiligte

• Bauschke, Heinz H.
• Dao, Minh N.
• Lindstrom, Scott B.

Titel

The Douglas–Rachford algorithm for a hyperplane and a doubleton

Ist Teil von

• Journal of global optimization, 2019-05, Vol.74 (1), p.79-93

Ort / Verlag

New York: Springer US

Erscheinungsjahr

2019

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• The Douglas–Rachford algorithm is a popular algorithm for solving both convex and nonconvex feasibility problems. While its behaviour is settled in the convex inconsistent case, the general nonconvex inconsistent case is far from being fully understood. In this paper, we focus on the most simple nonconvex inconsistent case: when one set is a hyperplane and the other a doubleton (i.e., a two-point set). We present a characterization of cycling in this case which—somewhat surprisingly—depends on whether the ratio of the distance of the points to the hyperplane is rational or not. Furthermore, we provide closed-form expressions as well as several concrete examples which illustrate the dynamical richness of this algorithm.