Abstract
This chapter and the following one offer a crash course in convex analysis, including the fundamental results in the theory of convex functions which are used throughout this book. In the present chapter, we review the Fenchel–Moreau–Rockafellar theory, giving new proofs highlighting the role of separation theorems. These results are then applied to provide dual representations of support functions, which are used in section 4.2 to develop a general duality theory for optimization. In this chapter, we also apply the Fenchel–Moreau–Rockafellar theorem to give slight non-convex extensions of the classical minimax theorems.
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Correa, R., Hantoute, A., López, M.A. (2023). Fenchel–Moreau–Rockafellar theory. In: Fundamentals of Convex Analysis and Optimization. Springer Series in Operations Research and Financial Engineering. Springer, Cham. https://doi.org/10.1007/978-3-031-29551-5_3
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DOI: https://doi.org/10.1007/978-3-031-29551-5_3
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Publisher Name: Springer, Cham
Print ISBN: 978-3-031-29550-8
Online ISBN: 978-3-031-29551-5
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