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Duality for Closed Convex Functions and Evenly Convex Functions
Journal of Optimization Theory and Applications, 2013We introduce two Moreau conjugacies for extended real-valued functions h on a separated locally convex space. In the first scheme, the biconjugate of h coincides with its closed convex hull, whereas, for the second scheme, the biconjugate of h is the evenly convex hull of h. In both cases, the biconjugate coincides with the supremum of the minorants of
Volle, M. +2 more
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Convex Sets and Convex Functions [PDF]
, 2011 We have encountered convex sets and convex functions on several occasions. Here we would like to discuss these notions in a more systematic way. Among nonlinear functions, the convex ones are the closest ones to the linear, in fact, functions that are convex and concave at the same time are just the linear affine functions.
Giuseppe Modica, Mariano Giaquinta
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Convex Sets and Convex Functions
2002This chapter explores sets that can be represented as intersections of (a possibly infinite number of) halfspaces of Rn . As will be shown, these are exactly the closed convex subsets. Furthermore, convex functions are studied, which are closely connected to convex sets and provide a natural generalization of linear functions.
Ulrich Faigle, Walter Kern, Georg Still
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Convex Sets and Convex Functions
2014Convex sets and functions have been studied since the nineteenth century; the twentieth century literature on convexity began with Bonnesen and Fenchel’s book [1], subsequently reprinted as [2].
Dan A. Simovici, Chabane Djeraba
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Convex Sets and Convex Functions [PDF]
, 1979 Because of their useful properties, the notions of convex sets and convex functions find many uses in the various areas of Applied Mathematics. We begin with the basic definition of a convex set in n-dimensional Euclidean Space (En), where points are ordered n-tuples of real numbers such as x’ = (x1, x2,…, xn) and y’ = (y1, y2,…,yn).
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Convex Sets and Convex Functions
2016The first chapter introduces the fundamental concepts and conclusions of functional analysis so that readers can have a foundation for going on reading this book successfully and can also understand notations used in the book. The arrangement of this chapter is as follows: The first section deals with normed linear spaces and inner product spaces which
Zhengzhi Han, Xiushan Cai, Jun Huang
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