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https://orion.math.iastate.edu/jdhsmith/math/SFGCS.pdf
support functions reflects exactly the modal structure on the compact convex sets given by convex combinations and convex hulls of unions. (See Section 3 below for an outline, and [4, 3.7] for details.) Given this algebraic approach to Minkowski’s support functions, and the fact that the set of all convex subsets ofRd forms a
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.
https://math.stackexchange.com/questions/1112262/support-function-of-a-set-is-convex
“Support function of a set” and supremum question. 0. ... What functions are support functions of convex sets. 1. The set of separating hyperplanes is a convex cone. 2. Is the support function always unique for a convex set? 1. Difference of support functions and its minimum points. 0.
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://en.wikipedia.org/wiki/Convex_functions
Convex functions play an important role in many areas of mathematics. They are especially important in the study of optimization problems where they are distinguished by a number of convenient properties. For instance, a strictly convex function on an open set has no more than one minimum.
https://www.stat.berkeley.edu/~aditya/resources/GUNTUBOYINA-2012-Optimal-Rates-of-Convergence-for-Convex-Set-Estimation-from-Support-Functions.pdf
CONVEX SET ESTIMATION FROM SUPPORT FUNCTIONS 387 In addition to the least squares estimator, Prince and Willsky [24] and Lele, Kulkarni and Willsky [19] also proposed estimators (in the case d =2) designed to take advantage of certain forms of prior knowledge, when available, about the true compact, convex set.
https://pdfs.semanticscholar.org/e373/7858dd3338a926d7f53a2b0708e704e64d50.pdf
Support Function Representation of Convex Bodies, Its Application in Geometric Computing, and Some Related Representations ... the support functions of the operand objects (Section 3). The support function, it is shown, can be viewed not as a single ... SUPPORT FUNCTION REPRESENTATION OF CONVEX BODIES 381 FIG. 2.
https://arxiv.org/pdf/1108.5341.pdf
OPTIMAL RATES OF CONVERGENCE FOR CONVEX SET ESTIMATION FROM SUPPORT FUNCTIONS By Adityanand Guntuboyina University of Pennsylvania We present a minimax optimal solution to the problem of esti-mating a compact, convex set from finitely many noisy measurements of its support function. The solution is based on appropriate regular-
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