The Forward–Backward Algorithm and the Normal Problem
| Autor: | Walaa M. Moursi |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
021103 operations research
Control and Optimization Applied Mathematics 0211 other engineering and technologies Forward–backward algorithm 010103 numerical & computational mathematics 02 engineering and technology Management Science and Operations Research Fixed point 01 natural sciences Displacement mapping Range (mathematics) Operator (computer programming) Monotone polygon Theory of computation Applied mathematics 0101 mathematics Mathematics |
| Zdroj: | Journal of Optimization Theory and Applications. 176:605-624 |
| ISSN: | 1573-2878 0022-3239 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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