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商品描述
This book provides a clear, modern, and application-driven introduction to mathematical optimization--one of the central technologies underlying today's data-driven decision making. Designed for students and practitioners encountering optimization for the first time, the book develops core concepts through intuitive explanations, concrete examples, and algorithmic insights, while maintaining mathematical rigor where it matters.
Beginning with smooth unconstrained problems, the text builds a unified framework connecting calculus, convexity, and optimality conditions. It progresses naturally to constrained and nonsmooth optimization, introducing subgradients, normal cones, and the Karush-Kuhn-Tucker condition in an accessible and coherent manner. Along the way, readers learn how fundamental algorithms--such as gradient, Newton's, and simplex methods--emerge from the underlying theory and how they behave in practice.
The book places strong emphasis on modeling, guiding readers from real-world problems to optimization formulations and solution strategies. Topics include linear and quadratic programming, network and integer structures, and optimization under uncertainty. Applications are drawn from engineering, operations research, data science, machine learning, and analytics, illustrating how optimization serves as a unifying language across disciplines.
Written as lecture notes for a one-semester introductory course, this book assumes only basic knowledge of calculus and linear algebra. It builds intuition, vocabulary, and mathematical comprehension, while largely avoiding formal proofs. Numerous worked examples, exercises, and fully solved problems support self-study and classroom use.
This book is ideal for advanced undergraduate students, master's students, and practitioners seeking a principled yet approachable introduction to optimization, as well as a foundation for further study in applied mathematics, operations research, and analytics.
商品描述(中文翻譯)
本書以清晰、現代且以應用為導向的方式，介紹數學最佳化（mathematical optimization）——這項技術是當今資料驅動決策的核心基礎之一。本書專為初次接觸最佳化的學生與實務工作者設計，透過直觀的說明、具體範例與演算法洞見，逐步建立核心概念，同時在重要之處維持數學嚴謹性。
從平滑無約束問題開始，本書建構出一套統一的架構，串聯微積分、凸性與最佳性條件。接著自然延伸至有約束與非光滑最佳化，以易於理解且前後一致的方式介紹次梯度（subgradient）、法錐（normal cone）以及 Karush-Kuhn-Tucker 條件。在學習過程中，讀者將了解梯度法、Newton 法與單純形法（simplex method）等基本演算法如何從底層理論中推導而來，以及它們在實務中的運作方式。
本書特別重視建模，引導讀者將真實世界的問題轉化為最佳化模型與解決策略。內容涵蓋線性規劃與二次規劃、網路與整數結構，以及不確定性下的最佳化。應用範例取材自工程、作業研究、資料科學、機器學習與分析，說明最佳化如何成為跨領域共通的語言。
本書以一學期入門課程的講義形式撰寫，讀者只需具備微積分與線性代數的基礎知識。全書著重於建立直覺、專業詞彙與數學理解，並大致避免形式化證明。大量的解題範例、習題與完整詳解，能支援讀者自學與課堂教學。
本書非常適合高年級大學生、碩士生，以及希望以嚴謹而易於理解的方式入門最佳化的實務工作者閱讀，也可作為進一步研習應用數學、作業研究與分析的基礎。
作者簡介
Dr. Johannes O. Royset is professor in the Daniel J. Epstein Department, University of Southern California. He was awarded a National Research Council postdoctoral fellowship in 2003, a Young Investigator Award from the Air Force Office of Scientific Research in 2007, and the Barchi Prize as well as the MOR Journal Award from the Military Operations Research Society in 2009. He received the Goodeve Medal from the Operational Research Society in 2019. Professor Royset was a plenary speaker at the International Conference on Stochastic Programming in 2016, the SIAM Conference on Uncertainty Quantification in 2018, and the INFORMS Security Conference in 2022. He has a PhD from UC Berkeley (2002). Professor Royset has been an associate or guest editor of several journals including SIAM Journal on Optimization, Operations Research, and Mathematical Programming. He has published two books and more than 100 articles.
作者簡介(中文翻譯)
Johannes O. Royset 博士是南加州大學 Daniel J. Epstein 系的教授。他於 2003 年獲頒 National Research Council 博士後研究獎學金，2007 年獲得 Air Force Office of Scientific Research 的 Young Investigator Award，並於 2009 年獲得 Military Operations Research Society 頒發的 Barchi Prize 及 MOR Journal Award。2019 年，他獲得 Operational Research Society 頒發的 Goodeve Medal。
Royset 教授曾在 2016 年 International Conference on Stochastic Programming、2018 年 SIAM Conference on Uncertainty Quantification，以及 2022 年 INFORMS Security Conference 擔任大會演講者。他於 2002 年取得 UC Berkeley 的博士學位。Royset 教授曾擔任多本期刊的副編輯或客座編輯，包括 SIAM Journal on Optimization、Operations Research 及 Mathematical Programming。他已出版兩本著作，並發表超過 100 篇論文。
