Basics of Nonlinear Optimization: Around the Weierstrass Theorem
暫譯: 非線性優化基礎：圍繞魏爾斯特拉斯定理
Galewski, Marek
- 出版商: Birkhauser Boston
- 出版日期: 2024-12-21
- 售價: $2,230
- 貴賓價: 9.5 折 $2,119
- 語言: 英文
- 頁數: 168
- 裝訂: Quality Paper - also called trade paper
- ISBN: 3031771591
- ISBN-13: 9783031771590
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商品描述
This textbook gives an introduction to optimization tools which arise around the Weierstrass theorem about the minimum of a lower semicontinuous function. Starting from a Euclidean space, it moves further into the infinite dimensional setting towards the direct variational method, going through differentiation and introducing relevant background information on the way.
Exercises accompany the text and include observations, remarks, and examples that help understand the presented material. Although some basic knowledge of functional analysis is assumed, covering Hilbert and Banach spaces and the Lebesgue integration, the required background material is covered throughout the text, and literature suggestions are provided. For less experienced readers, a summary of some optimization techniques is also included.
The book will appeal to both students and instructors in specialized courses on optimization, wishing to learn more about variational methods.
商品描述(中文翻譯)
這本教科書介紹了圍繞著 Weierstrass 定理的優化工具，該定理涉及下半連續函數的最小值。從歐幾里得空間開始，進一步探討無限維度的設定，朝向直接變分法發展，並在過程中介紹相關的背景資訊，包括微分等內容。
書中附有練習題，包含觀察、評論和範例，幫助理解所呈現的材料。雖然假設讀者具備一些基本的泛函分析知識，包括希爾伯特空間和巴拿赫空間以及勒貝格積分，但所需的背景材料在整本書中都有涵蓋，並提供了文獻建議。對於經驗較少的讀者，書中還包含了一些優化技術的摘要。
這本書將吸引希望深入了解變分方法的優化專業課程的學生和講師。
作者簡介
Marek Galewski has been a professor of mathematics at the Institute of Mathematics, Faculty of Technical Physics, Information Technology and Applied Mathematics, Lodz University of Technology since 2010. Between 1998-2010 he worked at the University of Lodz, first as instructor, then as assistant professor and from 2009 as associate professor. He works in nonlinear analysis with emphasis on boundary value problems investigated by variational and monotonicity methods. His current research concentrates on the interplay between variational and monotonicity methods.
作者簡介(中文翻譯)
Marek Galewski 自2010年以來一直擔任波茲南科技大學技術物理、資訊科技與應用數學學院數學研究所的數學教授。在1998年至2010年間，他在羅茲大學工作，最初擔任講師，然後擔任助理教授，並於2009年晉升為副教授。他的研究領域為非線性分析，重點在於通過變分法和單調性方法研究邊值問題。他目前的研究集中在變分法和單調性方法之間的相互作用。
