非线性优化的基本概念
This textbook is an introduction to nonlinear optimization, which treats mathematical concepts stringently on the one hand, but also motivates them in great detail and illustrates them with 42 figures. Therefore, the book is not only aimed at mathematicians, but also at natural scientists, engineers, and economists who want to understand and apply mathematically sound methods in their field. With just over two hundred pages, the book offers sufficient flexibility to serve as a foundation for various types of lectures on nonlinear optimization. Many geometric approaches for understanding both optimality conditions and numerical methods introduce a new perspective, enriching the existing literature on optimization. This is particularly evident in the detailed treatment of issues arising from different functional descriptions of the same geometry of feasible sets, and the thus motivated introduction of constraint qualifications for deriving derivative-based optimality conditions. This book is the English translation of the second edition of “Grundzüge der Nichtlinearen Optimierung” (Springer, 2021) written in German. The translation was done with the help of artificial intelligence. A subsequent revision was performed by the author to further refine the work and to ensure that the translation is appropriate concerning content and scientific correctness. It may, however, read stylistically different from a conventional translation.
中文|2024年9月17日|ISBN-10:3662697408|224页|Epub PDF（True）|22 MB这本教科书介绍了非线性优化，一方面严格对待数学概念，另一方面也非常详细地激励它们，并用42幅图加以说明。因此，这本书不仅面向数学家，也面向自然科学家、工程师和经济学家，他们希望在各自的领域理解和应用数学上合理的方法。这本书只有200多页，提供了足够的灵活性，可以作为各种非线性优化讲座的基础。许多用于理解最优性条件和数值方法的几何方法引入了一个新的视角，丰富了现有的优化文献。这在详细处理可行集的相同几何的不同函数描述所引起的问题时尤为明显，从而有动机引入约束条件来推导基于导数的最优性条件。这本书是德文版《优化生态系统的基本原理》（施普林格出版社，2021年）的英文译本。翻译是在人工智能的帮助下完成的。作者随后进行了修订，以进一步完善作品，并确保翻译在内容和科学正确性方面是恰当的。然而，它的阅读风格可能与传统翻译不同。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。
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