SURVEY: SIXTY YEARS OF DOUGLAS–RACHFORD

By Scott B. Lindstrom, Brailey Sims. 2018

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Abstract The Douglas–Rachford method is a splitting method frequently employed for finding zeros of sums of maximally monotone operators. When the operators in question are normal cone operators, the iterated process may be used to solve feasibility problems of the following form: Find $x\in \bigcap _{k=1}^{N}S_{k}$. The success of the method in the context of closed, convex, nonempty sets $S_{1},\ldots ,S_{N}$ is well known and understood from a theoretical standpoint. However, its performance in the nonconvex context is less well understood, yet it is surprisingly impressive. This was particularly compelling to Jonathan M. Borwein who, intrigued by Elser, Rankenburg and Thibault’s success in applying the method to solving sudoku puzzles, began an investigation of his own. We survey the current body of literature on the subject, and we summarize its history. We especially commemorate Professor Borwein’s celebrated contributions to the area.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Electrical and Electronic Engineering

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In Applied Mathematics

  1. René Vidal
  2. Paris V. Giampouras
  3. Liangzu Peng

In Computational Theory and Mathematics

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  2. Paris V. Giampouras
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In Electrical and Electronic Engineering

  1. René Vidal
  2. Paris V. Giampouras
  3. Liangzu Peng

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