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https://math.stackexchange.com/questions/235926/what-is-a-support-function-sup-z-in-k-langle-z-x-rangle
If you take $K$ to be convex, the support function is, in some sense, a tool for a dual representation of the set as the intersection of half-spaces. Let's assume that we're in $\mathbb R^n$ for simplicity.
https://www.encyclopediaofmath.org/index.php/Support_function
A support function is always convex, closed and positively homogeneous (of the first order). The operator is a one-to-one mapping from the family of closed convex sets in onto the family of closed convex homogeneous functions; the inverse operator is the subdifferential (at zero) of the support function.
https://orion.math.iastate.edu/jdhsmith/math/SFGCS.pdf
convex function is no longer convex.Thekeyalgebraic structure on R for use in the context of support functions comprises convex combinations forming a barycentric algebra (see [4]) and the maximum operation forming a join semilattice, the convex combinations distributing over the join so that the two structures combine to form
https://pdfs.semanticscholar.org/e373/7858dd3338a926d7f53a2b0708e704e64d50.pdf
scheme for convex bodies is the support function representation [3, 13, 29]. It was introduced by Minkowski in 1903, and has been extensively studied by mathematicians thereafter.
http://egrcc.github.io/docs/math/cvxbook-solutions.pdf
2.2 Show that a set is convex if and only if its intersection with any line is convex. Show that a set is a ne if and only if its intersection with any line is a ne. Solution. We prove the rst part. The intersection of two convex sets is convex. There-fore if Sis a convex set, the intersection of Swith a line is convex.
http://www-users.math.umn.edu/~lrotem/papers/supportalpha.pdf
1. Support functions and -concave functions A well known construction in classic convexity is the support function of a convex body. Let ;6= K Rn be a closed, convex set. Then its support function is a function h K: Rn!(1 ;1], de ned by h K(y) = sup x2K hx;yi; where h;idenotes the standard Euclidean structure on Rn. To begin our discussion, we will brie
http://home.ku.edu.tr/~emengi/papers/constrained_eigopt.pdf
A SUPPORT FUNCTION BASED ALGORITHM FOR OPTIMIZATION WITH EIGENVALUE CONSTRAINTS EMRE MENGIy Abstract. Optimization of convex functions subject to eigenvalue constraints is intriguing because of peculiar analytical properties of eigenvalue functions and is of practical interest because
https://en.wikipedia.org/wiki/Convex_function
In mathematics, a real-valued function defined on an n-dimensional interval is called convex if the line segment between any two points on the graph of the function lies above or on the graph. Equivalently, a function is convex if its epigraph is a convex set. For a twice-differentiable function of a single variable, if its second derivative is always nonnegative on its entire domain, then the function is convex. In fact, if …
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