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The Forward-Backward Algorithm and the Normal Problem.
- Source :
-
Journal of Optimization Theory & Applications . Mar2018, Vol. 176 Issue 3, p605-624. 20p. - Publication Year :
- 2018
-
Abstract
- The forward-backward splitting technique is a popular method for solving monotone inclusions that have applications in optimization. In this paper, we explore the behaviour of the algorithm when the inclusion problem has no solution. We present a new formula to define the normal solutions using the forward-backward operator. We also provide a formula for the range of the displacement map of the forward-backward operator. Several examples illustrate our theory. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00223239
- Volume :
- 176
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- Journal of Optimization Theory & Applications
- Publication Type :
- Academic Journal
- Accession number :
- 128397295
- Full Text :
- https://doi.org/10.1007/s10957-017-1113-4