Totally Convex Functions for Fixed Points Computation and Infinite Dimensional Optimization:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht
Springer Netherlands
2000
|
| Schriftenreihe: | Applied Optimization
40 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | The aim of this work is to present in a unified approach a series of results concerning totally convex functions on Banach spaces and their applications to building iterative algorithms for computing common fixed points of mea surable families of operators and optimization methods in infinite dimen sional settings. The notion of totally convex function was first studied by Butnariu, Censor and Reich [31] in the context of the space lRR because of its usefulness for establishing convergence of a Bregman projection method for finding common points of infinite families of closed convex sets. In this finite dimensional environment total convexity hardly differs from strict convexity. In fact, a function with closed domain in a finite dimensional Banach space is totally convex if and only if it is strictly convex. The relevancy of total convexity as a strengthened form of strict convexity becomes apparent when the Banach space on which the function is defined is infinite dimensional. In this case, total convexity is a property stronger than strict convexity but weaker than locally uniform convexity (see Section 1.3 below). The study of totally convex functions in infinite dimensional Banach spaces was started in [33] where it was shown that they are useful tools for extrapolating properties commonly known to belong to operators satisfying demanding contractivity requirements to classes of operators which are not even mildly nonexpansive |
| Beschreibung: | 1 Online-Ressource (XVI, 205 p) |
| ISBN: | 9789401140669 9789401057882 |
| ISSN: | 1384-6485 |
| DOI: | 10.1007/978-94-011-4066-9 |
Internformat
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| isbn | 9789401140669 9789401057882 |
| issn | 1384-6485 |
| language | English |
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| spelling | Butnariu, Dan Verfasser aut Totally Convex Functions for Fixed Points Computation and Infinite Dimensional Optimization by Dan Butnariu, Alfredo N. Iusem Dordrecht Springer Netherlands 2000 1 Online-Ressource (XVI, 205 p) txt rdacontent c rdamedia cr rdacarrier Applied Optimization 40 1384-6485 The aim of this work is to present in a unified approach a series of results concerning totally convex functions on Banach spaces and their applications to building iterative algorithms for computing common fixed points of mea surable families of operators and optimization methods in infinite dimen sional settings. The notion of totally convex function was first studied by Butnariu, Censor and Reich [31] in the context of the space lRR because of its usefulness for establishing convergence of a Bregman projection method for finding common points of infinite families of closed convex sets. In this finite dimensional environment total convexity hardly differs from strict convexity. In fact, a function with closed domain in a finite dimensional Banach space is totally convex if and only if it is strictly convex. The relevancy of total convexity as a strengthened form of strict convexity becomes apparent when the Banach space on which the function is defined is infinite dimensional. In this case, total convexity is a property stronger than strict convexity but weaker than locally uniform convexity (see Section 1.3 below). The study of totally convex functions in infinite dimensional Banach spaces was started in [33] where it was shown that they are useful tools for extrapolating properties commonly known to belong to operators satisfying demanding contractivity requirements to classes of operators which are not even mildly nonexpansive Mathematics Functional analysis Integral equations Operator theory Discrete groups Mathematical optimization Calculus of Variations and Optimal Control; Optimization Convex and Discrete Geometry Functional Analysis Operator Theory Integral Equations Mathematik Fixpunkttheorie (DE-588)4293945-8 gnd rswk-swf Konvexe Funktion (DE-588)4139679-0 gnd rswk-swf Optimierung (DE-588)4043664-0 gnd rswk-swf Konvexe Funktion (DE-588)4139679-0 s Fixpunkttheorie (DE-588)4293945-8 s Optimierung (DE-588)4043664-0 s 1\p DE-604 Iusem, Alfredo N. Sonstige oth https://doi.org/10.1007/978-94-011-4066-9 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Butnariu, Dan Totally Convex Functions for Fixed Points Computation and Infinite Dimensional Optimization Mathematics Functional analysis Integral equations Operator theory Discrete groups Mathematical optimization Calculus of Variations and Optimal Control; Optimization Convex and Discrete Geometry Functional Analysis Operator Theory Integral Equations Mathematik Fixpunkttheorie (DE-588)4293945-8 gnd Konvexe Funktion (DE-588)4139679-0 gnd Optimierung (DE-588)4043664-0 gnd |
| subject_GND | (DE-588)4293945-8 (DE-588)4139679-0 (DE-588)4043664-0 |
| title | Totally Convex Functions for Fixed Points Computation and Infinite Dimensional Optimization |
| title_auth | Totally Convex Functions for Fixed Points Computation and Infinite Dimensional Optimization |
| title_exact_search | Totally Convex Functions for Fixed Points Computation and Infinite Dimensional Optimization |
| title_full | Totally Convex Functions for Fixed Points Computation and Infinite Dimensional Optimization by Dan Butnariu, Alfredo N. Iusem |
| title_fullStr | Totally Convex Functions for Fixed Points Computation and Infinite Dimensional Optimization by Dan Butnariu, Alfredo N. Iusem |
| title_full_unstemmed | Totally Convex Functions for Fixed Points Computation and Infinite Dimensional Optimization by Dan Butnariu, Alfredo N. Iusem |
| title_short | Totally Convex Functions for Fixed Points Computation and Infinite Dimensional Optimization |
| title_sort | totally convex functions for fixed points computation and infinite dimensional optimization |
| topic | Mathematics Functional analysis Integral equations Operator theory Discrete groups Mathematical optimization Calculus of Variations and Optimal Control; Optimization Convex and Discrete Geometry Functional Analysis Operator Theory Integral Equations Mathematik Fixpunkttheorie (DE-588)4293945-8 gnd Konvexe Funktion (DE-588)4139679-0 gnd Optimierung (DE-588)4043664-0 gnd |
| topic_facet | Mathematics Functional analysis Integral equations Operator theory Discrete groups Mathematical optimization Calculus of Variations and Optimal Control; Optimization Convex and Discrete Geometry Functional Analysis Operator Theory Integral Equations Mathematik Fixpunkttheorie Konvexe Funktion Optimierung |
| url | https://doi.org/10.1007/978-94-011-4066-9 |
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