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Epigraph of a function A function (in black) is convex if and only if the region above its graph (in green) is a convex set.This region is the function's epigraph. In mathematics, the epigraph or supergraph [1] of a function: [,] valued in the extended real numbers [,] = {} is the set = {(,) : ()} consisting of all points in the Cartesian product lying on or above the function's graph. [2]
Hypograph of a function. In mathematics, the hypograph or subgraph of a function: is the set of points lying on or below its graph. A related definition is that of such a function's epigraph, which is the set of points on or above the function's graph.
Menards sold the Menard Building Division in 1994, racking up 36 years in the pole building industry. Menards of East Madison, Wisconsin, pictured in 2012 (closed and relocated to Sun Prairie in 2018) [6] Menards was founded as Menard Cashway Lumber. In the mid-1980s, the "Cashway Lumber" name was dropped and the business became simply known to ...
Given a relation on pairs of elements of set and an element of . The upper contour set of is the set of all that are related to : { }The lower contour set of is the set of all such that is related to them:
Hypograph may refer to: Hypograph (mathematics) , the set of points lying below the graph of a function Hypograph, or hypogram, something written at the end of a document (for example, a postscript )
Undirected hypergraphs are useful in modelling such things as satisfiability problems, [5] databases, [6] machine learning, [7] and Steiner tree problems. [8] They have been extensively used in machine learning tasks as the data model and classifier regularization (mathematics). [9]
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