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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© 2011 Springer Science+Business Media, LLC
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Bauschke, H.H., Combettes, P.L. (2011). Lower Semicontinuous Convex Functions. In: Convex Analysis and Monotone Operator Theory in Hilbert Spaces. CMS Books in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-9467-7_9
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DOI: https://doi.org/10.1007/978-1-4419-9467-7_9
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Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-9466-0
Online ISBN: 978-1-4419-9467-7
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