参数变分系统的局部强极大单调性和完全稳定性
Local strong maximal monotonicity and full stability for parametric variational systems
摘要：
本文引入并刻画了作用在希尔伯特空间中由偏次微分和法锥映射描述的一般参数变分系统解的Lipschitz和Hölderian完全稳定性的新概念.这些概念假设了解映射的单值局部化的某些定量性质，与相关集值映射的局部强极大单调性密切相关。基于变分分析和广义微分的先进工具，我们得到了可验证的特征的局部强极大单调性和充分的稳定性概念考虑通过一些正定性条件，涉及二阶变分分析的建设。所得到的一般结果是指定的重要类的变分不等式和变分条件在有限和无限维。
英文摘要：
The paper introduces and characterizes new notions of Lipschitzian and Hölderian full stability of solutions to general parametric variational systems described via partial subdifferential and normal cone mappings acting in Hilbert spaces. These notions, postulated certain quantitative properties of single-valued localizations of solution maps, are closely related to local strong maximal monotonicity of associated set-valued mappings. Based on advanced tools of variational analysis and generalized differentiation, we derive verifiable characterizations of the local strong maximal monotonicity and full stability notions under consideration via some positive-definiteness conditions involving second-order constructions of variational analysis. The general results obtained are specified for important classes of variational inequalities and variational conditions in both finite and infinite dimensions.
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