Optimization in Banach spaces [electronic resource]

• 作者： Zaslavski, Alexander J.
• 其他作者：
  • SpringerLink (Online service)
• 其他題名：
  • SpringerBriefs in optimization.
• 出版： Cham : Springer International Publishing :Imprint: Springer
• 叢書名： SpringerBriefs in optimization,
• 主題： Mathematical optimization. , Banach spaces. , Optimization. , Numerical Analysis.
• ISBN： 9783031126444 (electronic bk.) 、 9783031126437 (paper)
• FIND@SFXID: CGU
• 資料類型: 電子書
• 內容註: Preface -- Introduction -- Convex optimization -- Nonconvex optimization -- Continuous algorithms -- References.
• More
• 摘要註: 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 optimization problem in a general Banach space the situation becomes more difficult and less understood. On the other hand such problems arise in the approximation theory. The book is of interest for mathematicians working in optimization. It also can be useful in preparation courses for graduate students. The main feature of the book which appeals specifically to this audience is the study of algorithms for convex and nonconvex minimization problems in a general Banach space. The book is of interest for experts in applications of optimization to the approximation theory. In this book the goal is to obtain a good approximate solution of the constrained optimization problem in a general Banach space under the presence of computational errors. It is shown that the algorithm generates a good approximate sol
• 讀者標籤：

  需登入
• 引用連結：

  Copy Link
• 目前引用數
• Share: