Titlebook: Convex Analysis and Monotone Operator Theory in Hilbert Spaces; Heinz H. Bauschke,Patrick L. Combettes Book 2017Latest edition Springer In

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Virtual Worlds as Philosophical Tools positively homogeneous functions are also presented. Also discussed are the Moreau–Rockafellar theorem, which characterizes coercivity in terms of an interiority condition, and the Toland–Singer theorem, which provides an appealing formula for the conjugate of a difference.

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concise

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https://doi.org/10.1057/9781137508416omposition based on closed linear subspaces. They also arise naturally in convex analysis in the local study of a convex set via the tangent cone and the normal cone operators, and they are central in the analysis of various extensions of the notion of an interior that will be required in later chapters.

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https://doi.org/10.1057/9781137519269detail in this chapter. In particular, it is shown that the conjugate of an infimal convolution is the sum of the conjugates. The key result of this chapter is the Fenchel–Moreau theorem, which states that the proper convex lower semicontinuous functions are precisely those functions that coincide with their biconjugates.

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Convex Sets,asserts that every nonempty closed convex subset . of . is a Chebyshev set, i.e., that every point in . possesses a unique best approximation from ., and which provides a characterization of this best approximation.

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