Local Monotonicity and Full Stability for Parametric Variational Systems
本文针对有限维和希尔伯特空间中由近正则函数的次微分定义的参数变分系统，引入并刻画了Lipschitz和Hölder完全稳定性的新概念，通过二阶构造的正定性条件给出了局部强极大单调性和完全稳定性的可验证特征。
This paper introduces and characterizes new notions of Lipschitzian and Hölderian full stability of solutions to general parametric variational systems defined via partial subdifferential of prox-regular functions acting in finite-dimensional and Hilbert spaces. These notions, which postulate 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.