Convex Optimization (Hardcover)

Stephen Boyd, Lieven Vandenberghe

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<內容簡介>

 

Convex optimization problems arise frequently in many different fields. This book provides a comprehensive introduction to the subject, and shows in detail how such problems can be solved numerically with great efficiency. The book begins with the basic elements of convex sets and functions, and then describes various classes of convex optimization problems. Duality and approximation techniques are then covered, as are statistical estimation techniques. Various geometrical problems are then presented, and there is detailed discussion of unconstrained and constrained minimization problems, and interior-point methods. The focus of the book is on recognizing convex optimization problems and then finding the most appropriate technique for solving them. It contains many worked examples and homework exercises and will appeal to students, researchers and practitioners in fields such as engineering, computer science, mathematics, statistics, finance and economics.

>Gives comprehensive details on how to recognize convex optimization problems in a wide variety of settings
>Provides a broad range of practical algorithms for solving real problems
>Contains hundreds of worked examples and homework exercises

<章節目錄>

 

Preface
1. Introduction
Part I. Theory:
2. Convex sets
3. Convex functions
4. Convex optimization problems
5. Duality
Part II. Applications:
6. Approximation and fitting
7. Statistical estimation
8. Geometrical problems
Part III. Algorithms:
9. Unconstrained minimization
10. Equality constrained minimization
11. Interior-point methods
Appendices

 

商品描述(中文翻譯)

內容簡介:

凸優化問題在許多不同領域中經常出現。本書全面介紹了這個主題,並詳細展示了如何以高效的方式數值解決這些問題。書籍首先介紹了凸集和凸函數的基本要素,然後描述了各種類型的凸優化問題。接著介紹了對偶性和逼近技術,以及統計估計技術。然後介紹了各種幾何問題,並詳細討論了無約束和有約束最小化問題以及內點法。本書的重點是識別凸優化問題,並找到最適合解決這些問題的技術。書中包含許多實例和作業練習,適用於工程、計算機科學、數學、統計、金融和經濟等領域的學生、研究人員和從業人員。

- 在各種不同情境中如何識別凸優化問題的全面細節
- 提供了解決實際問題的廣泛算法
- 包含數百個實例和作業練習

章節目錄:

前言
1. 引言
第一部分. 理論:
2. 凸集
3. 凸函數
4. 凸優化問題
5. 對偶性
第二部分. 應用:
6. 逼近和擬合
7. 統計估計
8. 幾何問題
第三部分. 算法:
9. 無約束最小化
10. 等式約束最小化
11. 內點法
附錄