Abstract
The theory of convex functions is most powerful in the presence of lower semicontinuity. A key property of lower semicontinuous convex functions is the existence of a continuous affine minorant, which we establish in this chapter by projecting onto the epigraph of the function.
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14 January 2020
The original version of this book was inadvertently published without updating the following corrections in Chapters 1, 2, 3, 6–13, 17, 18, 20, 23, 24, 26, 29, 30 and back matter. These are corrected now.
References
R. B. Ash, Real Analysis and Probability, Academic Press, New York, 1972.
S. Simons, Minimax and Monotonicity, vol. 1693 of Lecture Notes in Mathematics, Springer-Verlag, Berlin, 1998.
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Bauschke, H.H., Combettes, P.L. (2017). Lower Semicontinuous Convex Functions. In: Convex Analysis and Monotone Operator Theory in Hilbert Spaces. CMS Books in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-48311-5_9
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DOI: https://doi.org/10.1007/978-3-319-48311-5_9
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