| 书目名称 | Optimization in Banach Spaces |
| 编辑 | Alexander J. Zaslavski |
| 视频video | |
| 概述 | Studies convex optimization problems in a general Banach space under the presence of computational errors.Studies nonconvex optimization problems in a general Banach space under the presence of comput |
| 丛书名称 | SpringerBriefs in Optimization |
| 图书封面 |  |
| 描述 | The book is devoted to the study of constrained minimization problems on closed and convex sets in Banach spaces with a Frechet differentiable objective function. Such problems are well studied in a finite-dimensional space and in an infinite-dimensional Hilbert space. When the space is Hilbert there are many algorithms for solving optimization problems including the gradient projection algorithm which is one of the most important tools in the optimization theory, nonlinear analysis and their applications. An optimization problem is described by an objective function and a set of feasible points. For the gradient projection algorithm each iteration consists of two steps. The first step is a calculation of a gradient of the objective function while in the second one we calculate a projection on the feasible set. In each of these two steps there is a computational error. In our recent research we show that the gradient projection algorithm generates a good approximate solution, if all the computational errors are bounded from above by a small positive constant. It should be mentioned that the properties of a Hilbert space play an important role. When we consider an optimizat |
| 出版日期 | Book 2022 |
| 关键词 | Banach space; constrained minimization problem; Hilbert space; approximation theory; nonconvex optimizat |
| 版次 | 1 |
| doi | https://doi.org/10.1007/978-3-031-12644-4 |
| isbn_softcover | 978-3-031-12643-7 |
| isbn_ebook | 978-3-031-12644-4Series ISSN 2190-8354 Series E-ISSN 2191-575X |
| issn_series | 2190-8354 |
| copyright | The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl |
发表于 2025-3-21 20:01:03
