An Easy Path to Convex Analysis and Applications (Paperback)

Boris S. Mordukhovich, Nguyen Mau Nam

  • 出版商: Morgan & Claypool
  • 出版日期: 2013-12-01
  • 定價: $1,750
  • 售價: 9.0$1,575
  • 語言: 英文
  • 頁數: 218
  • 裝訂: Paperback
  • ISBN: 1627052372
  • ISBN-13: 9781627052375
  • 立即出貨 (庫存=1)

商品描述

Convex optimization has an increasing impact on many areas of mathematics, applied sciences, and practical applications. It is now being taught at many universities and being used by researchers of different fields. As convex analysis is the mathematical foundation for convex optimization, having deep knowledge of convex analysis helps students and researchers apply its tools more effectively. The main goal of this book is to provide an easy access to the most fundamental parts of convex analysis and its applications to optimization. Modern techniques of variational analysis are employed to clarify and simplify some basic proofs in convex analysis and build the theory of generalized differentiation for convex functions and sets in finite dimensions. We also present new applications of convex analysis to location problems in connection with many interesting geometric problems such as the Fermat-Torricelli problem, the Heron problem, the Sylvester problem, and their generalizations. Of course, we do not expect to touch every aspect of convex analysis, but the book consists of sufficient material for a first course on this subject. It can also serve as supplemental reading material for a course on convex optimization and applications.

Table of Contents: Preface / Acknowledgments / List of Symbols / Convex Sets and Functions / Subdifferential Calculus / Remarkable Consequences of Convexity / Applications to Optimization and Location Problems / Solutions and Hints for Exercises / Bibliography / Authors' Biographies / Index

商品描述(中文翻譯)

凸優化在數學、應用科學和實際應用領域中的影響越來越大。現在許多大學都開設了相關課程,並被不同領域的研究人員使用。由於凸分析是凸優化的數學基礎,深入了解凸分析有助於學生和研究人員更有效地應用其工具。本書的主要目標是提供對凸分析及其在優化中的應用的最基本部分的易於理解的介紹。現代變分分析技術被用來澄清和簡化凸分析中一些基本證明,並建立有限維凸函數和集合的廣義微分理論。我們還介紹了凸分析在與許多有趣的幾何問題相關的位置問題中的新應用,例如費馬-托里切利問題、海龍問題、西爾維斯特問題及其推廣問題。當然,我們並不打算觸及凸分析的每個方面,但本書包含了足夠的材料作為第一門課程的補充。它也可以作為凸優化和應用課程的參考讀物。

目錄: 前言 / 致謝 / 符號列表 / 凸集和凸函數 / 次微分計算 / 凸性的顯著結果 / 優化和位置問題的應用 / 練習題解答和提示 / 參考文獻 / 作者簡介 / 索引