An Easy Path to Convex Analysis and Applications
Mordukhovich, Boris, Nam, Nguyen Mau
- 出版商: Springer
- 出版日期: 2024-05-17
- 售價: $1,980
- 貴賓價: 9.5 折 $1,881
- 語言: 英文
- 頁數: 300
- 裝訂: Quality Paper - also called trade paper
- ISBN: 3031264606
- ISBN-13: 9783031264603
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商品描述
This book examines the most fundamental parts of convex analysis and its applications to optimization and location problems. Accessible techniques of variational analysis are employed to clarify and simplify some basic proofs in convex analysis and to build a theory of generalized differentiation for convex functions and sets in finite dimensions. The book serves as a bridge for the readers who have just started using convex analysis to reach deeper topics in the field. Detailed proofs are presented for most of the results in the book and also included are many figures and exercises for better understanding the material. Applications provided include both the classical topics of convex optimization and important problems of modern convex optimization, convex geometry, and facility location.
商品描述(中文翻譯)
本書探討凸分析的最基本部分及其在優化和位置問題中的應用。使用可變分分析的可行技術，以澄清和簡化凸分析中的一些基本證明，並建立凸函數和有限維凸集的廣義微分理論。本書為剛開始使用凸分析的讀者提供了一座通往更深入主題的橋樑。書中大多數結果都提供了詳細的證明，並包含了許多圖片和練習，以更好地理解材料。提供的應用包括傳統的凸優化主題以及現代凸優化、凸幾何和設施位置的重要問題。
作者簡介
Boris Mordukhovich, PhD, is Distinguished University Professor of Mathematics at Wayne State University. He has more than 500 publications including several monographs. Among his best known achievements are the introduction and development of powerful constructions of generalized differentiation and their applications to broad classes of problems in variational analysis, optimization, equilibrium, control, economics, engineering, and other fields. Dr. Mordukhovich is a SIAM Fellow, an AMS Fellow, and a recipient of many international awards and honors including Doctor Honoris Causa degrees from six universities over the world. He is a Highly Cited Researcher in Mathematics. His research has been supported by continued grants from the National Science Foundations and the Air Force Office of Scientific Research.
Nguyen Mau Nam, PhD, is Professor of Mathematics at Portland State University. He has published more than 60 research articles and one book in convex analysiswith applications to optimization theory and numerical algorithms. He has received several awards for his research including a best paper award by Journal of Global Optimization in 2021 and the Columbia-Willamette Chapter of Sigma Xi Outstanding Researcher Award in Mathematical Sciences in 2015. His research was supported by grants from the National Science Foundation, the Simons Foundation, and Portland State University.
Nguyen Mau Nam, PhD, is Professor of Mathematics at Portland State University. He has published more than 60 research articles and one book in convex analysiswith applications to optimization theory and numerical algorithms. He has received several awards for his research including a best paper award by Journal of Global Optimization in 2021 and the Columbia-Willamette Chapter of Sigma Xi Outstanding Researcher Award in Mathematical Sciences in 2015. His research was supported by grants from the National Science Foundation, the Simons Foundation, and Portland State University.
作者簡介(中文翻譯)
Boris Mordukhovich博士是韋恩州立大學數學系的傑出大學教授。他發表了500多篇論文，包括幾本專著。他最著名的成就之一是引入和發展了強大的廣義微分構造，並將其應用於變分分析、優化、均衡、控制、經濟、工程和其他領域的廣泛問題。Mordukhovich博士是SIAM Fellow、AMS Fellow，並獲得了許多國際獎項和榮譽，包括來自世界各地的六所大學頒發的名譽博士學位。他是數學領域的高被引研究者。他的研究得到了美國國家科學基金會和空軍科學研究辦公室的持續資助。
Nguyen Mau Nam博士是波特蘭州立大學數學系的教授。他發表了60多篇研究論文和一本關於凸分析在優化理論和數值算法中應用的書籍。他的研究獲得了多個獎項，包括2021年《全球優化期刊》的最佳論文獎和2015年哥倫比亞-威拉米特分會Sigma Xi數學科學傑出研究者獎。他的研究得到了美國國家科學基金會、Simons基金會和波特蘭州立大學的資助。
