Fundamentals of Convex Analysis
Fundamentals of Convex Analysis
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DOI：
10.1007/978-3-642-56468-0
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发表时间：
2004-06
期刊：
影响因子：
56.9
通讯作者：
J. Hiriart-Urruty;C. Lemaréchal
中科院分区：
文献类型：
--
作者：
J. Hiriart-Urruty;C. Lemaréchal
这本书是我们的两卷本《凸分析和最小化算法》[18]的删节版，自从1993年由Springer-Verlag出版以来，我们已经收到了来自用户，读者和讲师的非常积极的反馈。它的教学质量特别受到赞赏，并与相当先进的技术材料相结合。现在[18]双重但明确定义的性质：-介绍凸分析的基本概念，-凸最小化问题的研究（强调数值算法），并坚持它们的相互渗透。我们认为，科学界非常需要上述基本介绍。这是本版本的动机，我们的意图是创建一个有用的工具，教凸分析。因此，我们从[18]中提取了专门用于凸分析的”主干”，即第三章至第六章和第十章。除了一些地方的改进，目前的案文主要是相应章节的副本。主要的区别是，我们删除了被认为太先进的介绍，或太密切地连接到数值算法的材料。此外，我们还包括练习，其难度由0，I或2星 * 建议。最后，指数得到了极大的丰富。就像在[18]中一样，每一章都被呈现为一堂“课”，从我们老大师的意义上来说，完整地对待给定的主题。
This book is an abridged version of our two-volume opus Convex Analysis and Minimization Algorithms [18], about which we have received very positive feedback from users, readers, lecturers ever since it was published-by Springer-Verlag in 1993. Its pedagogical qualities were particularly appreciated, in the combination with a rather advanced technical material. Now [18] hasa dual but clearly defined nature:-an introduction to the basic concepts in convex analysis,-a study of convex minimization problems (with an emphasis on numerical al-rithms), and insists on their mutual interpenetration. It is our feeling that the above basic introduction is much needed in the scientific community. This is the motivation for the present edition, our intention being to create a tool useful to teach convex anal ysis. We have thus extracted from [18] its" backbone" devoted to convex analysis, namely ChapsIII-VI and X. Apart from some local improvements, the present text is mostly a copy of the corresponding chapters. The main difference is that we have deleted material deemed too advanced for an introduction, or too closely attached to numerical algorithms. Further, we have included exercises, whose degree of difficulty is suggested by 0, I or 2 stars*. Finally, the index has been considerably enriched. Just as in [18], each chapter is presented as a" lesson", in the sense of our old masters, treating of a given subject in its entirety.