Fundamentals of Convex Analysis and Optimization: A Supremum Function Approach

Correa, Rafael, Hantoute, Abderrahim, López, Marco A.

Fundamentals of Convex Analysis and Optimization: A Supremum Function Approach
  • 出版商: Springer
  • 出版日期: 2024-07-12
  • 售價: $2,170
  • 貴賓價: 9.5 折 $2,062
  • 語言: 英文
  • 頁數: 444
  • 裝訂: Quality Paper - also called trade paper
  • ISBN: 3031295536
  • ISBN-13: 9783031295539

    • 海外代購書籍(需單獨結帳)

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商品描述

This book aims at an innovative approach within the framework of convex analysis and optimization, based on an in-depth study of the behavior and properties of the supremum of families of convex functions. It presents an original and systematic treatment of convex analysis, covering standard results and improved calculus rules in subdifferential analysis. The tools supplied in the text allow a direct approach to the mathematical foundations of convex optimization, in particular to optimality and duality theory. Other applications in the book concern convexification processes in optimization, non-convex integration of the Fenchel subdifferential, variational characterizations of convexity, and the study of Chebychev sets. At the same time, the underlying geometrical meaning of all the involved concepts and operations is highlighted and duly emphasized. A notable feature of the book is its unifying methodology, as well as the novelty of providing an alternative or complementary viewto the traditional one in which the discipline is presented to students and researchers.

This textbook can be used for courses on optimization, convex and variational analysis, addressed to graduate and post-graduate students of mathematics, and also students of economics and engineering. It is also oriented to provide specific background for courses on optimal control, data science, operations research, economics (game theory), etc. The book represents a challenging and motivating development for those experts in functional analysis, convex geometry, and any kind of researchers who may be interested in applications of their work.


商品描述(中文翻譯)

本書旨在於凸分析與優化的框架內採取創新的方法，基於對凸函數族的上確界行為和性質的深入研究。它提供了對凸分析的原創且系統性的處理，涵蓋了標準結果和改進的次微分分析計算規則。書中提供的工具使得對凸優化的數學基礎，特別是最優性和對偶理論，能夠進行直接的探討。書中的其他應用涉及優化中的凸化過程、Fenchel 次微分的非凸積分、凸性的變分特徵以及Chebychev集合的研究。同時，所有相關概念和操作的基本幾何意義也得到了突顯和強調。本書的一個顯著特點是其統一的方法論，以及提供一種替代或補充傳統觀點的新穎性，這種觀點通常是向學生和研究人員介紹該學科的方式。

本教科書可用於優化、凸分析和變分分析的課程，適合數學的研究生和碩士生，以及經濟學和工程學的學生。它也旨在為最優控制、數據科學、運籌學、經濟學（博弈論）等課程提供特定的背景。本書對於功能分析、凸幾何的專家以及任何對其工作應用感興趣的研究人員來說，都是一個具有挑戰性和激勵性的發展。

作者簡介

Rafael Correa, Mathematical Engineering Degree from the University of Chile (1971), Doctor in Engineering, University of Clermont, France (1974) and Doctor in Mathematics Science, Blaise Pascal University, France (1984). He served as Executive Director of CONICYT, the Chilean National Agency for Scientific Research and Development (1990-1994), as Founder and Director of the Mathematical Modeling Center (CMM) at the University of Chile (2000-2007), and as President of O'Higgins University Chile, since its foundation in 2015. Author of fifty papers on Mathematical Optimization and Variational Analysis.
Abderrahim Hantoute, Doctor in Applied Mathematics from Université Paul Sabatier de Toulouse (2003), Postdoc Fellowship in Alicante and Elche Universities 2004-2007, Associate researcher (at CMM, Universidad de Chile until 2020, and then at Universidad de Alicante). According to MathSciNet: 47 papers, with 316 citations by 182authors.
Marco A. López, Doctor in Mathematics from Valencia University (1973), Full Professor since 1981, currently at Alicante University as Emeritus Professor. Doctor Honoris Causa by the University of Limoges (2012), Honorary Adjunct Professor of Federation University, Australia (2013), as and Corresponding Member of the Real Academia de Ciencias of Spain (2014). Research on mathematical optimization, semi-infinite programming, variational analysis and game theory. According to MathSciNet: 151 papers, with 1788 citations by 590 authors.

作者簡介(中文翻譯)

拉斐爾·科雷亞（Rafael Correa），智利大學數學工程學位（1971），法國克萊蒙大學工程博士（1974）及法國布萊茲·帕斯卡大學數學科學博士（1984）。曾擔任智利國家科學研究與發展機構（CONICYT）執行董事（1990-1994），智利大學數學建模中心（CMM）創始人及主任（2000-2007），以及自2015年成立以來的智利奧伊金斯大學校長。著有五十篇有關數學優化和變分分析的論文。

阿卜德拉希姆·漢圖特（Abderrahim Hantoute），法國圖盧茲保羅·薩巴捷大學應用數學博士（2003），於阿利坎特和埃爾切大學進行2004-2007年的博士後研究，曾擔任智利大學CMM的副研究員（直到2020年），之後在阿利坎特大學任職。根據MathSciNet的資料：發表47篇論文，獲得182位作者的316次引用。

馬爾科·A·洛佩斯（Marco A. López），瓦倫西亞大學數學博士（1973），自1981年起擔任正教授，目前為阿利坎特大學名譽教授。獲得利摩日大學榮譽博士（2012），澳大利亞聯邦大學名譽副教授（2013），以及西班牙皇家科學院通訊會員（2014）。研究領域包括數學優化、半無限規劃、變分分析和博弈論。根據MathSciNet的資料：發表151篇論文，獲得590位作者的1788次引用。

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