Titlebook: Lectures on Variational Analysis; Asen L. Dontchev Book 2021 The Editor(s) (if applicable) and The Author(s), under exclusive license to S

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978-3-030-79913-7The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl

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Lectures on Variational Analysis978-3-030-79911-3Series ISSN 0066-5452 Series E-ISSN 2196-968X

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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.

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Mappings with Convex Graphs,e simplest example of such a mapping is any linear and bounded mapping . : . → . ; indeed, the graph of such a mapping is a closed linear subspace in . × . . More generally, any mapping of the form . + ., where . : . → .  is linear and bounded and . ⊂ .  is a closed convex set and has closed and con

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The Constrained Linear-Quadratic Optimal Control Problem,se lectures, we focus on a basic optimal control problem, which consists in minimizing a quadratic integral functional over a finite time interval, for a linear control system with control constrained to a closed and convex set.

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