Abstract
We have already seen, in the First order sufficient condition (2.1.2), one benefit of convexity in optimization: critical points of convex functions are global minimizers. In this section we extend the types of functions we consider in two important ways:
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(i)
We do not require f to be differentiable.
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(ii)
We allow f to take the value + ∞.
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© 2000 Springer Science+Business Media New York
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Borwein, J.M., Lewis, A.S. (2000). Fenchel Duality. In: Convex Analysis and Nonlinear Optimization. CMS Books in Mathematics / Ouvrages de mathématiques de la SMC. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-9859-3_3
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DOI: https://doi.org/10.1007/978-1-4757-9859-3_3
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4757-9861-6
Online ISBN: 978-1-4757-9859-3
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