线性与非线性规划，第四版

English | PDF,EPUB | 2016 | 547 Pages | ISBN : 3319188410 | 10.66 MB

This new edition covers the central concepts of practical optimization techniques, with an emphasis on methods that are both state-of-the-art and popular. One major insight is the connection between the purely analytical character of an optimization problem and the behavior of algorithms used to solve a problem. This was a major theme of the first edition of this book and the fourth edition expands and further illustrates this relationship. As in the earlier editions, the material in this fourth edition is organized into three separate parts. Part I is a self-contained introduction to linear programming. The presentation in this part is fairly conventional, covering the main elements of the underlying theory of linear programming, many of the most effective numerical algorithms, and many of its important special applications. Part II, which is independent of Part I, covers the theory of unconstrained optimization, including both derivations of the appropriate optimality conditions and an introduction to basic algorithms. This part of the book explores the general properties of algorithms and defines various notions of convergence. Part III extends the concepts developed in the second part to constrained optimization problems. Except for a few isolated sections, this part is also independent of Part I. It is possible to go directly into Parts II and III omitting Part I, and, in fact, the book has been used in this way in many universities. New to this edition is a chapter devoted to Conic Linear Programming, a powerful generalization of Linear Programming. Indeed, many conic structures are possible and useful in a variety of applications. It must be recognized, however, that conic linear programming is an advanced topic, requiring special study. Another important topic is an accelerated steepest descent method that exhibits superior convergence properties, and for this reason, has become quite popular. The proof of the convergence property for both standard and accelerated steepest descent methods are presented in Chapter 8. As in previous editions, end-of-chapter exercises appear for all chapters. From the reviews of the Third Edition “… this very well-written book is a classic textbook in Optimization. It should be present in the bookcase of each student, researcher, and specialist from the host of disciplines from which practical optimization applications are drawn.” (Jean-Jacques Strodiot, Zentralblatt MATH, Vol. 1207, 2011)

这新版涵盖了实用优化技术的核心概念，重点在于既是最前沿又很受欢迎的方法。一个主要的洞见是优化问题的纯粹分析特性与用于解决问题的算法行为之间的联系。这是本书上一版的一个主要主题，并且第四版进一步扩展和阐释了这种关系。正如前几版一样，第四版的内容分为三个独立的部分。第一部分是一套自包含的线性规划介绍。这一部分内容比较常规，涵盖了线性规划基础理论的主要要素、许多最有效的数值算法，以及许多重要的特殊应用。第二部分（与第一部分独立）介绍了无约束优化理论，包括适当的最优条件推导和基本算法简介。这部分探讨了算法的一般性质，并定义了一些收敛的概念。第三部分将前两部分所开发的概念扩展到约束优化问题上。除了少数孤立的章节外，这一部分也与第一部分相对独立。实际上，许多大学就是采用这样的方式来使用这本书的。新版新增一章专门讨论锥形线性规划，这是一种强大的一般化线性规划的方法。的确，许多锥结构在各种应用中都是可能且有用的。然而必须认识到的是，锥形线性规划是一个高级主题，需要特殊研究。另一个重要的话题是加速梯度下降法，它展示出非常优秀的收敛特性，并因此而变得很受欢迎。标准和加速梯度下降方法的收敛性质的证明出现在第八章里。正如前几版一样，每一章后面都配有习题。《第三版》评论：“这本书写得很不错，是一本经典的优化教材。每一个应用实际优化问题的学生、研究者及专业人士都应该拥有一本。”（Jean-Jacques Strodiot，《数学文摘》，Vol. 1207, 2011年）

---

Download from free file storage

 Download from upfiles.com  Download from userupload.net  Download from nitroflare.com  Download from rapidgator.net

---

我要反馈

---

本站不对文件进行储存，仅提供文件链接，请自行下载，本站不对文件内容负责，请自行判断文件是否安全，如发现文件有侵权行为，请联系管理员删除。