加花粗鄙人
发表于 2025-3-23 12:26:07
Derivative Criteria for Metric Regularity,In this lecture, we will characterize metric regularity by using generalized derivatives of set-valued mappings. To make things simpler, we limit our considerations to mappings in Euclidean spaces. Some of the results can be extended to infinite dimensions but we will not do that here.
间接
发表于 2025-3-23 14:53:16
Strong Regularity,We begin this lecture with a basic theorem in analysis: the classical inverse function theorem.
平常
发表于 2025-3-23 19:57:54
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美色花钱
发表于 2025-3-23 22:30:09
Nonsmooth Inverse Function Theorems,The classical inverse function theorems assume continuous differentiability of the function involved.
滔滔不绝地说
发表于 2025-3-24 03:45:10
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一起平行
发表于 2025-3-24 07:18:51
Strong Subregularity,“One-point” variants of the property of metric regularity can be obtained if in the definition we fix one of the points . or . at the reference values . or .. Specifically, consider a mapping . acting between metric spaces and . in the graph of ..
FLAIL
发表于 2025-3-24 13:25:21
Continuous Selections,The classical inverse function theorem presented in Lecture . gives conditions under which the inverse of a function has a single-valued localization, that is, locally, the inverse is a function.
Gleason-score
发表于 2025-3-24 14:57:57
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栏杆
发表于 2025-3-24 22:42:13
Regularity in Nonlinear Control,In this lecture we consider a control system described by a nonlinear ordinary differential equation of the form . over the interval . Here, as for the linear-quadratic problem in the preceding lecture, .(.) ∈ .. is the state of the system, while .(.) ∈ .. is the control, both at time ..
figment
发表于 2025-3-25 01:58:45
Metric Regularity, follows . and . are metric spaces with metrics that are denoted in the same way by .(⋅, ⋅) but may be different. Recall that a set . in a metric space is . at a point . ∈ . when there exists a neighborhood . of . such that the intersection . ∩ . is a closed set.