Variational analysis and generalized differentiation
Variational analysis and generalized differentiation
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DOI：
10.1007/3-540-31247-1
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发表时间：
2006
期刊：
影响因子：
--
通讯作者：
B. Mordukhovich
中科院分区：
文献类型：
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作者：
B. Mordukhovich
变分分析被认为是数学中一个富有成果的领域，它一方面处理优化和平衡问题的研究，另一方面应用优化、摄动和近似思想来分析可能不具有变分性质的广泛问题。现代变分分析最显著的特征之一是固有的非光滑性，它不仅自然地通过优化相关问题的初始数据进入，而且在很大程度上通过变分原理和摄动技术进入。因此，广义微分是变分分析及其应用的核心。本专著对有限维和无限维空间的变分分析和广义微分的基本概念和原理进行了全面和最新的研究，并在优化、平衡、稳定性和灵敏度、控制理论、经济学、力学等问题上提出了许多应用。本书分两卷出版，第一卷主要介绍变分分析和广义微分的基本理论，第二卷包含各种应用。两卷都包含丰富的参考书目和广泛的评论。
Variational analysis has been recognized as a fruitful area in mathematics that on the one hand deals with the study of optimization and equilibrium problems and on the other hand applies optimization, perturbation, and approximation ideas to the analysis of a broad range of problems that may not be of a variational natur. One of the most characteristic features of modern variational analysis is the intrinsic presence of nonsmoothness, which naturally enters not only through initial data of optimization-related problems but largely via variational principles and perturbation techniques. Thus generalized differential lies at the hear of variational analysis and its applications.This monographs contains a comprehensive and and state-of-the art study of the basic concepts and principles of variational analysis and generalized differentiation in both finite-dimensional and infinite dimensional spaces and presents numerous applications to problems in the optimization, equilibria, stability and sensitivity, control theory, economics, mechanics, etc. The book is published in two volumes, the first of which is mainly devoted to the basic theory of variational analysis and generalized differentiations, while the second volume contains various applications. Both volumes contain abundant bibliographies and extensive commentaries.