Guy Bouchitte
Published 2020-04-20Version 1
Convexity is an important notion in non linear optimization theory as well as in infinite dimensional functional analysis. As will be seen below, very simple and powerful tools will be derived from elementary duality arguments (which are byproducts of the Moreau-Fenchel transform and Hahn Banach Theorem). We will emphasize on applications to a large range of variational problems. Some arguments of measure theory will be skipped.
Journal: Encyclopedia of Mathematical physics, Academic Press (2006), pp.642-652
More on the Concept of Duality in Convex Analysis, the Characterizations of Fenchel Transform and Identity
General monotonicity
The Kreps-Yan theorem for $L^\infty$
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