登入選單
返回Google圖書搜尋
Totally Convex Functions for Fixed Points Computation and Infinite Dimensional Optimization
Dan ButnariuAlfredo N. Iusem
出版Springer Science & Business Media, 2000
主題Mathematics / Algebra / GeneralMathematics / AppliedMathematics / Geometry / GeneralMathematics / Linear & Nonlinear ProgrammingMathematics / Mathematical AnalysisMathematics / Functional AnalysisMathematics / OptimizationMedical / GeneralTechnology & Engineering / Manufacturing
ISBN079236287X9780792362876
URLhttp://books.google.com.hk/books?id=evy11snQWGQC&hl=&source=gbs_api
EBookSAMPLE
註釋The main purpose of this book is to present, in a unified approach, several algorithms for fixed point computation, convex feasibility and convex optimization in infinite dimensional Banach spaces, and for problems involving, eventually, infinitely many constraints. For instance, methods like the simultaneous projection algorithm for feasibility, the proximal point algorithm and the augmented Lagrangian algorithm are rigorously formulated and analyzed in this general setting and shown to be applicable to much wider classes of problems than previously known. For this purpose, a new basic concept, total convexity, is introduced. Its properties are deeply explored, and a comprehensive theory is presented, bringing together previously unrelated ideas from Banach space geometry, finite dimensional convex optimization and functional analysis. For making a general approach possible the work aims to improve upon classical results like the Holder-Minkowsky inequality of ℒp.