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Titlebook: Direct Methods in Control Problems; Peter Falb Textbook 2019 Springer Science+Business Media, LLC, part of Springer Nature 2019 Lévy proce

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楼主: 喝水
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Derivatives and Solutions,We often consider control problems for systems defined by “differential” equations (ordinary, partial or stochastic) and we require an appropriate notion of differentiation and what constitutes a solution.
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Minimization of Functionals: Hilbert Spaces,We shall generalize this result in Chapter 6. The key elements in the proof are the invertibility of a linear transformation (.(.) here) and the use of the Implicit Function Theorem.
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Minimization of Functionals: Uniformly Convex Spaces,We want to prove an analogy of Theorem 4.27 for these (Sobolev) gradients in so-called uniformly convex spaces.
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Minimization of Functionals: Hilbert Space, 2,We saw in Chapter 2 that these problems are equivalent in that . is a solution of 6.3 if and only if . is a solution of 6.4.
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Optimization of Functionals: Necessary Conditions,We recall the notions of differentiablilty for maps of Banach spaces.
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