Introduction to Nonlinear Optimization: Theory, Algorithms, and Applications ...

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Introduction to Nonlinear Optimization: Theory, Algorithms, and Applications with MATLAB Amir Beck“非线性优化简介：MATLAB中的理论，算法和应用” 英文| 2014 | ISBN：1611973643 | 294页| PDF | 3 MB 本书提供了非线性优化理论的基础以及一些相关的算法，并提出了应用科学各个领域的各种应用。作者综合了优化理论与算法基础三个支柱，熟悉各种应用，以及将理论与算法应用于实际问题的能力，严格，逐步建立了理论，算法，应用与实现之间的联系。 读者将发现超过170种理论，算法和数值练习，深化和增强读者对主题的理解。作者包括优化书中通常没有的几个主题 - 例如稀疏约束优化，隐藏凸度和总最小二乘法中的最优条件。本书还提供了理论和算法上讨论的大量应用，如圆形拟合，切比雪夫中心，费马 - 韦伯问题，去噪，聚类，总最小二乘和正交回归以及MATLAB工具箱CVX演示的理论和算法主题以及一张贴在书籍网站上的m文件。 读者：本书适用于数学，计算机科学，电气工程以及其他工程部门的研究生或高级本科生。这本书也是研究人员感兴趣的。 内容：第1章：数学初步;第2章：无约束优化的优化条件;第3章：最小二乘法;第四章梯度法第五章牛顿法第6章：凸集;第七章：凸函数第8章：凸优化;第9章：凸集优化;第10章：线性约束问题的最优条件;第11章：KKT条件;第12章：双重性 Amir Beck, "Introduction to Nonlinear Optimization: Theory, Algorithms, and Applications with MATLAB" English | 2014 | ISBN: 1611973643 | 294 pages | PDF | 3 MB This book provides the foundations of the theory of nonlinear optimization as well as some related algorithms and presents a variety of applications from diverse areas of applied sciences. The author combines three pillars of optimization-theoretical and algorithmic foundation, familiarity with various applications, and the ability to apply the theory and algorithms on actual problems-and rigorously and gradually builds the connection between theory, algorithms, applications, and implementation. Readers will find more than 170 theoretical, algorithmic, and numerical exercises that deepen and enhance the reader's understanding of the topics. The author includes several subjects not typically found in optimization books-for example, optimality conditions in sparsity-constrained optimization, hidden convexity, and total least squares. The book also offers a large number of applications discussed theoretically and algorithmically, such as circle fitting, Chebyshev center, the Fermat-Weber problem, denoising, clustering, total least squares, and orthogonal regression and theoretical and algorithmic topics demonstrated by the MATLAB toolbox CVX and a package of m-files that is posted on the book's web site. Audience: This book is intended for graduate or advanced undergraduate students of mathematics, computer science, and electrical engineering as well as other engineering departments. The book will also be of interest to researchers. Contents: Chapter 1: Mathematical Preliminaries; Chapter 2: Optimality Conditions for Unconstrained Optimization; Chapter 3: Least Squares; Chapter 4: The Gradient Method; Chapter 5: Newton s Method; Chapter 6: Convex Sets; Chapter 7: Convex Functions; Chapter 8: Convex Optimization; Chapter 9: Optimization Over a Convex Set; Chapter 10: Optimality Conditions for Linearly Constrained Problems; Chapter 11: The KKT Conditions; Chapter 12: Duality