| 書目名稱 | Totally Convex Functions for Fixed Points Computation and Infinite Dimensional Optimization |
| 編輯 | Dan Butnariu,Alfredo N. Iusem |
| 視頻video | http://file.papertrans.cn/927/926660/926660.mp4 |
| 叢書名稱 | Applied Optimization |
| 圖書封面 |  |
| 描述 | 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 |
| 出版日期 | Book 2000 |
| 關(guān)鍵詞 | Banach Space; Convexity; Dimension; Integral equation; Optimal control; algorithms; control; functional ana |
| 版次 | 1 |
| doi | https://doi.org/10.1007/978-94-011-4066-9 |
| isbn_softcover | 978-94-010-5788-2 |
| isbn_ebook | 978-94-011-4066-9Series ISSN 1384-6485 |
| issn_series | 1384-6485 |
| copyright | Springer Science+Business Media Dordrecht 2000 |
|Archiver|手機版|小黑屋|
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