Abstract
The Douglas–Rachford (DR) algorithm is an iterative procedure that uses sequential reflections onto convex sets and which has become popular for convex feasibility problems. In this paper we propose a structural generalization that allows to use r-sets-DR operators in a cyclic fashion. We prove convergence and present numerical illustrations of the potential advantage of such operators with r>2 over the classical 2-sets-DR operators in a cyclic algorithm.
Original language | English |
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Pages (from-to) | 875-889 |
Number of pages | 15 |
Journal | Optimization Methods and Software |
Volume | 34 |
Issue number | 4 |
DOIs | |
State | Published - 4 Jul 2019 |
Bibliographical note
Funding Information:The f irst author was supported by MINECO of Spain and ERDF of EU, as part of the Ramón y Cajal program (RYC-2013-13327) and the Grant MTM2014-59179-C2-1-P. The second author’s work was supported by research grant no. 2013003 of the United States-Israel Binational Science Foundation (BSF). The third author’s work was supported by the EU FP7 IRSES program STREVCOMS, grant no. PIRSES-GA-2013-612669.
Publisher Copyright:
© 2018, © 2018 Informa UK Limited, trading as Taylor & Francis Group.
Keywords
- Douglas–Rachford
- feasibility problems
- r-sets-Douglas–Rachford operator
- reflections
ASJC Scopus subject areas
- Software
- Control and Optimization
- Applied Mathematics