Titlebook: Convex Analysis and Monotone Operator Theory in Hilbert Spaces; Heinz H. Bauschke,Patrick L. Combettes Book 2017Latest edition Springer In

ligature

Vandalism and Anti-Social BehaviourIn this chapter we present variants of the notion of convexity for functions. The most important are the weaker notion of quasiconvexity and the stronger notions of uniform and strong convexity.

Decrepit

Coma704

https://doi.org/10.1057/9781137519269This chapter is devoted to a fundamental convexity-preserving operation for functions: the infimal convolution..Special attention is given to the Moreau envelope and the proximity operator.

思考而得

Virtual Worlds as Philosophical ToolsOf central importance in convex analysis are conditions guaranteeing that the conjugate of a sum is the infimal convolution of the conjugates. The main result in this direction is a theorem due to Attouch and Brézis. In turn, it gives rise to the Fenchel–Rockafellar duality framework for convex optimization problems.

衰弱的心

Jargon

單色

即席

Support Functions and Polar Sets,In this chapter, we develop basic results concerning support points, including the Bishop–Phelps theorem and the representation of a nonempty closed convex set as the intersection of the closed half-spaces containing it. Polar sets are also studied.

使入迷

Convex Functions,Convex functions, which lie at the heart of modern optimization, are introduced in this chapter. We study operations that preserve convexity and the interplay between various continuity properties.

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