The magnitude of the minimal displacement vector for compositions and convex combinations of firmly nonexpansive mappings
| Autor: | Walaa M. Moursi, Heinz H. Bauschke |
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| Rok vydání: | 2018 |
| Předmět: |
Pure mathematics
021103 operations research Control and Optimization 0211 other engineering and technologies Regular polygon Magnitude (mathematics) 010103 numerical & computational mathematics 02 engineering and technology Fixed point 01 natural sciences Displacement (vector) Nonlinear system Monotone polygon 0101 mathematics Mathematics |
| Zdroj: | Optimization Letters. 12:1465-1474 |
| ISSN: | 1862-4480 1862-4472 |
| Popis: | Maximally monotone operators and firmly nonexpansive mappings play key roles in modern optimization and nonlinear analysis. Five years ago, it was shown that if finitely many firmly nonexpansive operators are all asymptotically regular (i.e., they have or “almost have” fixed points), then the same is true for compositions and convex combinations. In this paper, we derive bounds on the magnitude of the minimal displacement vectors of compositions and of convex combinations in terms of the displacement vectors of the underlying operators. Our results completely generalize earlier works. Moreover, we present various examples illustrating that our bounds are sharp. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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