Theory and Methods of Optimisation
暫譯: 優化的理論與方法

Carpignani, Andrea, Pappalardo, Massimo

Theory and Methods of Optimisation
  • 出版商: Springer
  • 出版日期: 2026-02-14
  • 售價: $2,860
  • 貴賓價: 9.5 折 $2,717
  • 語言: 英文
  • 頁數: 261
  • 裝訂: Quality Paper - also called trade paper
  • ISBN: 3032015138
  • ISBN-13: 9783032015136
  • 相關分類: 工程數學 Engineering-mathematics

    • 海外代購書籍(需單獨結帳)

相關主題

商品描述

This book originates from the graduate course Theory and Methods of Optimisation taught at the University of Pisa and is primarily intended for students seeking a rigorous yet accessible introduction to optimisation techniques. While designed with graduate students in mind, the text is largely self-contained and may also be approached by motivated undergraduates with a solid foundation in mathematical analysis, linear algebra, and the basic topology of Euclidean spaces. Key results from differential calculus and topology are recalled throughout, ensuring that the material remains accessible without compromising mathematical depth.
Structured in three parts, the text offers a coherent progression from foundational theory to algorithmic methods. The first part provides an introduction to convex analysis; the second covers the theory of linear and nonlinear programming; and the third presents key classical algorithms, including the simplex method and gradient-based techniques. Each chapter builds on previous material, with methods presented in detail, including pseudocode and full convergence proofs.
Throughout, the book combines theoretical rigour with applied insight. Every result is proved, and numerous worked examples illustrate the methods in action. This dual emphasis gives the work the character of both a rigorous theoretical text and a practical guide to mathematical optimisation.

The book serves both as an introduction and as a comprehensive reference for those interested in applying mathematical models to real-world problems. It will be especially valuable to young researchers in applied mathematics looking to understand the theoretical underpinnings of optimisation methods as well as to those working on the practical implementation of such techniques.

商品描述(中文翻譯)

這本書源自比薩大學所教授的研究生課程《優化理論與方法》，主要針對尋求嚴謹但易於理解的優化技術入門的學生。雖然設計時考慮了研究生，但本書內容大部分是自成體系的，對於具備數學分析、線性代數及歐幾里得空間基本拓撲學基礎的有動力的本科生也適用。書中不斷回顧微積分和拓撲學的關鍵結果，確保材料在不妨礙數學深度的情況下仍然易於理解。

本書分為三個部分，提供從基礎理論到算法方法的連貫進展。第一部分介紹凸分析；第二部分涵蓋線性和非線性規劃的理論；第三部分介紹關鍵的經典算法，包括單純形法和基於梯度的技術。每一章都在前一章的基礎上進行擴展，詳細介紹方法，包括偽代碼和完整的收斂證明。

整本書結合了理論的嚴謹性與應用的洞察力。每個結果都有證明，並且有許多實例展示方法的實際應用。這種雙重重點使得本書既具備嚴謹的理論文本特徵，又是數學優化的實用指南。

本書既可作為入門書籍，也可作為對於有興趣將數學模型應用於現實問題的全面參考資料。對於希望理解優化方法理論基礎的應用數學年輕研究者，以及從事這些技術實際實施的人士，將特別有價值。

作者簡介

Andrea Carpignani graduated from the University of Pisa in March 2005, with a dissertation focused on the applications of stochastic calculus to partial differential equations. His academic interests are measure theory and integration, convex and functional analysis, probability, mathematical statistics, and data science. Following four years as a teaching assistant at the University of Pisa, Andrea Carpignani pursued a career in secondary and further education, teaching Mathematics and Physics in the province of Florence. Since relocating to the United Kingdom in 2017, he has taught mathematics at secondary, post-16, and further education levels, undertaking roles including Subject Specialist for Key Stage 5 Mathematics, Head of Mathematics, and currently Key Stage 5 Coordinator at the Radcliffe School in Milton Keynes.

Massimo Pappalardo is a full professor of Operations Research. After graduation "cum laude" in Mathematics at the University of Pisa, he did his Ph.D. in Mathematics. Since 1988, he was first an associate professor and then, a full professor of Operations Research. He has taught in the Faculty of Engineering, in the Faculty of Science and in the Faculty of Economics. He was the director of the Department of Applied Mathematics, President of the degree course in Computer Science and President of the "Academic Quality Control". In 2023, he was awarded the order of the cherub, the highest honour of the University of Pisa for full professors. His scientific interests lie in optimisation, variational analysis and equilibrium problems both from a theoretical and applicative point of view. He is the author of more than 80 papers in international journals. He wrote two didactical books and a research book in the Springer Operations Research series.

作者簡介(中文翻譯)

安德烈亞·卡皮尼亞尼於2005年3月畢業於比薩大學，論文專注於隨機微積分在偏微分方程中的應用。他的學術興趣包括測度理論與積分、凸分析與泛函分析、概率論、數學統計以及數據科學。在比薩大學擔任四年的教學助理後，安德烈亞·卡皮尼亞尼開始了中等及進一步教育的職業生涯，在佛羅倫斯省教授數學和物理。自2017年搬遷至英國以來，他在中學、16歲以上及進一步教育層級教授數學，擔任過關鍵階段5數學科目專家、數學系主任，目前是米爾頓·凱恩斯的拉德克利夫學校的關鍵階段5協調員。

馬西莫·帕帕拉多是運籌學的全職教授。在比薩大學以優異成績畢業後，他獲得數學博士學位。自1988年以來，他先是擔任副教授，然後成為運籌學的全職教授。他曾在工程學院、科學學院和經濟學院授課。他曾擔任應用數學系主任、計算機科學學位課程主任以及「學術質量控制」的主席。2023年，他獲得比薩大學全職教授的最高榮譽——天使勳章。他的科學興趣包括優化、變分分析和均衡問題，從理論和應用的角度進行研究。他在國際期刊上發表了超過80篇論文，並撰寫了兩本教學書籍和一本在Springer運籌學系列中的研究書籍。

類似商品