Optimization
暫譯: 優化

Lange, Kenneth

Optimization
  • 出版商: Springer
  • 出版日期: 2015-04-03
  • 售價: $5,640
  • 貴賓價: 9.8 折 $5,527
  • 語言: 英文
  • 頁數: 529
  • 裝訂: Quality Paper - also called trade paper
  • ISBN: 1489992707
  • ISBN-13: 9781489992703
  • 相關分類: 工程數學 Engineering-mathematics

    • 海外代購書籍(需單獨結帳)

商品描述

Finite-dimensional optimization problems occur throughout the mathematical sciences. The majority of these problems cannot be solved analytically. This introduction to optimization attempts to strike a balance between presentation of mathematical theory and development of numerical algorithms. Building on students' skills in calculus and linear algebra, the text provides a rigorous exposition without undue abstraction. Its stress on statistical applications will be especially appealing to graduate students of statistics and biostatistics. The intended audience also includes students in applied mathematics, computational biology, computer science, economics, and physics who want to see rigorous mathematics combined with real applications.

In this second edition the emphasis remains on finite-dimensional optimization. New material has been added on the MM algorithm, block descent and ascent, and the calculus of variations. Convex calculus is now treated in much greater depth. Advanced topics such as the Fenchel conjugate, subdifferentials, duality, feasibility, alternating projections, projected gradient methods, exact penalty methods, and Bregman iteration will equip students with the essentials for understanding modern data mining techniques in high dimensions.

商品描述(中文翻譯)

有限維優化問題在數學科學中隨處可見。大多數這些問題無法通過解析方法解決。本書對優化的介紹試圖在數學理論的呈現與數值算法的發展之間取得平衡。該文本建立在學生的微積分和線性代數技能之上，提供了嚴謹的闡述而不過於抽象。其對統計應用的強調將特別吸引統計學和生物統計學的研究生。預期的讀者還包括應用數學、計算生物學、計算機科學、經濟學和物理學的學生，他們希望看到嚴謹的數學與實際應用相結合。

在第二版中，重點仍然放在有限維優化上。新增了有關MM算法、區塊下降和上升以及變分法的材料。凸微積分現在得到了更深入的處理。高級主題如Fenchel共軛、次微分、對偶性、可行性、交替投影、投影梯度法、精確懲罰法和Bregman迭代將使學生掌握理解高維數據挖掘技術的基本要素。

作者簡介

Kenneth Lange is the Rosenfeld Professor of Computational Genetics at UCLA. He is also Chair of the Department of Human Genetics and Professor of Biomathematics and Statistics. At various times during his career, he has held appointments at the University of New Hampshire, MIT, Harvard, the University of Michigan, the University of Helsinki, and Stanford. He is a fellow of the American Statistical Association, the Institute of Mathematical Statistics, and the American Institute for Medical and Biomedical Engineering. His research interests include human genetics, population modeling, biomedical imaging, computational statistics, and applied stochastic processes. Springer previously published his books Mathematical and Statistical Methods for Genetic Analysis, Numerical Analysis for Statisticians, and Applied Probability, all in second editions.

作者簡介(中文翻譯)

肯尼斯·蘭格（Kenneth Lange）是加州大學洛杉磯分校（UCLA）計算遺傳學的羅森菲爾德教授。他同時擔任人類遺傳學系主任及生物數學與統計學教授。在他的職業生涯中，他曾在新罕布什爾大學、麻省理工學院（MIT）、哈佛大學、密西根大學、赫爾辛基大學和史丹佛大學擔任職位。他是美國統計協會（American Statistical Association）、數學統計學會（Institute of Mathematical Statistics）和美國醫學與生物醫學工程學會（American Institute for Medical and Biomedical Engineering）的會士。他的研究興趣包括人類遺傳學、族群建模、生物醫學影像、計算統計學和應用隨機過程。施普林格（Springer）之前出版了他的書籍《遺傳分析的數學與統計方法》（Mathematical and Statistical Methods for Genetic Analysis）、《統計學家的數值分析》（Numerical Analysis for Statisticians）和《應用概率》（Applied Probability），均為第二版。

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