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Jingdong book

信息技术和电气工程学科国际知名教材中译本系列：非线性规划（第2版）

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Jingdong book

信息技术和电气工程学科国际知名教材中译本系列：非线性规划（第2版）

Name: 信息技术和电气工程学科国际知名教材中译本系列：非线性规划（第2版）
Brand: Jingdong book
SKU: 3101011461
Price: 51.69 USD
Availability: OutOfStock

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本书系统全面地介绍了非线性规划的理论和方法，是学习、研究相关理论和方法的重要教材和学术著作。
本书从无约束优化问题入手，通过直观分析和严谨证明给出了无约束优化问题的zui优性条件，并讨论了梯度法、牛顿法、共轭方向法等实用算法。
本书将深层次的优化理论分析与实用的计算方法密切结合，以解决各种不同类型的优化问题。
本书可以作为高年级本科生、研究生运筹优化类课程教材或者相关研究者、工程师的工具参考书。

Content Description

《信息技术和电气工程学科国际知名教材中译本系列：非线性规划（第2版）》涵盖了非线性规划的主要内容，包括无约束优化、凸优化、拉格朗日乘子理论和算法、对偶理论和方法等，并包含了大量的实际应用案例。《信息技术和电气工程学科国际知名教材中译本系列：非线性规划（第2版）》从无约束优化问题入手，通过直观分析和严谨证明给出了无约束优化问题的优性条件，并讨论了梯度法、牛顿法、共轭方向法等实用算法。进而本书将无约束优化问题的优性条件和算法推广到具有凸集约束的优化问题中，进一步讨论了处理约束问题的可行方向法、条件梯度法、梯度投影法、双矩阵投影法、坐标块下降法等算法。拉格朗日乘子理论和算法是非线性规划的核心内容之一，也是本书的重点。本书中的第3、4章详尽地论述了这方面的内容。本书首先从等式约束优化问题优解的必要条件入手，给出了拉格朗日乘子理论基本的形式，然后给出了等式约束优化问题优解的充分条件以及不等式约束优化问题的充分条件和必要条件。拉格朗日乘子算法的引入则基于将约束优化问题转化为无约束优化问题和求解优性条件对应的方程组两个角度展开，分别讨论了障碍函数法、惩罚函数法、序贯二次规划法、拉格朗日法和原始对偶内点法等方法，本书的另一个重点是对偶理论和方法，本书第5章从几何的角度阐述了拉格朗日对偶理论和Fenchel对偶理论，并讨论了离散优化及拉格朗日松弛方法；本书最后一章则详细讨论了求解对偶问题的相关概念和方法，包括次梯度、对偶上升方法、次梯度方法、割平面方法和分解方法等。

Catalogue

第1章无约束优化
1.1 最优性条件
1.1.1 主要的最优性条件
1.2 梯度方法的收敛性
1.2.1 下降方向和步长准则
1.2.2 收敛结果
1.3 梯度方法的收敛速率
1.3.1 局部分析方法
1.3.2 条件数的作用
1.3.3 关于收敛速率的结论
1.4 牛顿方法及其变形
1.5 最小二乘问题
1.5.1 高斯一牛顿方法
1.5.2 增量梯度法
1.5.3 高斯一牛顿法的增量形式
1.6 共轭方向法
1.7 拟牛顿法
1.8 非求导方法
1.8.1 坐标下降法
1.8.2 直接搜索法
1.9 离散时间最优控制问题
1.10 一些实用的指导准则
1.11 注释和参考资料

第2章凸集优化
2.1 约束优化问题
2.1.1 最优解的充要条件
2.1.2 最优解的存在性+
2.2 可行方向法和条件梯度法
2.2.1 下降方向和步长规则
2.2.2 条件梯度法
2.3 梯度投影法
2.3.1 基于投影方法的可行方向和步长规则
2.3.2 收敛性分析
2.4 双矩阵投影方法
2.5 流型子优化方法
2.6 线性规划的仿射变换
2.7 坐标块下降方法
2.8 注释和参考资料

第3章拉格朗日乘子理论
3.1 等式约束优化问题的必要条件
3.1.1 惩罚法
3.1.2 消元法
3.1.3 拉格朗日函数
3.2 等式约束优化问题的充分条件和灵敏度分析
3.2.1 增广的拉格朗日方法
3.2.2 可行方向法
3.2.3 灵敏度+
3.3 不等式约束优化问题
3.3.1 Karush-Kuhn-Tucker最优性条件
3.3.2 转化为等式约束处理
3.3.3 二阶充分条件和灵敏度
3.3.4 充分性条件及拉格朗曰最小化
3.3.5 FritzJohn最优性条件
3.3.6 深化和精练
3.4 线性约束和对偶性
3.4.1 凸目标函数和线性约束
3.4.2 对偶理论：针对简单等式约束的优化问题
3.5 注释和参考资料

第4章拉格朗日乘子算法
第5章对偶性与凸规划
第6章对偶方法
附录A 数学背景
附录B 凸分析
附录C 线性搜索方法
附录D 牛顿法的运用
参考文献

Introduction

作者 Dimitri P. Bertsekas曾在希腊雅典国立技术大学机械和电子工程系学习，并在麻省理工学院获得系统科学专业博士学位.
作者先后在斯坦福大学、伊利诺伊大学执教，并自 1979年开始，任教于麻省理工学院，现任该系 McAfee教授. Bertsekas教授经常为工业界提供相关咨询服务，并担任众多期刊的编委工作 .Bertsekas教授研究领域广泛，包括优化理论、控制理论、大规模计算和数据通信网络等领域，并发表众多研究论文，同时著有 13本教材和研究专著.
Bertsekas教授凭借其与 John Tsitsikli在运筹优化和计算科学交叉领域的合作专著 Neuro-Dynamic Programming的杰出研究而获得 1997年 INFORMS奖，同时 Bertsekas教授还先后获得了 2000年希腊国家运筹优化奖和 2001年 ACC John R. Ragazzini教育奖.2000年，他被评为美国国家工程院院士 .
作者的其他著作包括：
1. Programming and Stochastic Control, Academic Press, 1976.
2. Stochastic Optimal Control: The Discrete-Time Case, Academic Press, 1978.本书由 Athena Scienti.c出版社于 1997年再版 (合著者为 S. E. Shreve；已翻译为俄语).
3. Constrained Optimization and Lagrange Multiplier Methods, Academic Press, 1982.本书由 Athena Scienti.c出版社于 1996年再版 (已翻译为俄语).
4. Dynamic Programming: Deterministic and Stochastic Models, Prentice Hall, 1987.
5. Data Networks, Prentice Hall, 1987.1992年出版第二版 (合著者为 R. G. Gallager;已翻译为俄语和日语).
6. Parallel and Distributed Computation: Numerical Methods, Prentice Hall, 1989.本书由 Athena Scienti.c出版社于 1997年再版 (合著者为 J. N. Tsitsiklis).
7. Linear Network Optimization: Algorithms and Codes, M.I.T. Press, 1991.
8. Dynamic Programming and Optimal Control, 2 Vols., Athena Scienti.c, 1995.
9. Neuro-Dynamic Programming, Athena Scienti.c, 1996 (合著者为 J. N. Tsitsiklis).
10. Network Optimization: Continuous and Discrete Models, Athena Scienti.c, 1998.
11. Introduction to Probability, Athena Scienti.c, 2002 (合著者为 J. N. Tsitsiklis).
12. Convex Analysis and Optimization, Athena Scienti.c, 2003 (合著者为 A. Nedic和 A. E. Ozdaglar).

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