Results 311 to 320 of about 463,586 (333)

Convexity with convex combinations

Antarctica Journal of Mathematics, 2013
The paper refers to convexity in the space using the vector algebra supported with the geometrical images. The work relies on the properties of the basic convex sets in the plane and space, polygons and polyhedra. The well-known results are presented by using the convex and affine combinations.
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Convex and anti-convex languages

International Journal of Computer Mathematics, 1998
We define here the counterpart of Jensen convex and anti-convex sets of real numbers for the case of languages. We investigate the existence of languages consisting only of strings in which a set of symbols is convex or anti-convex, as well as the place of such languages in Chomsky hierarchy. Local convexity is also briefly investigated.
Jürgen Dassow, Gheorghe Paun, Solomon Marcus   +2 more
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Convex Sets and Convex Functions

2002
This 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

2014
Convex 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 Optimization With Convex Constraints

2001
In this chapter we want to solve the problem minf(x) | x ∈ C, where f is a convex function on ℝ n , and C is a convex, nonempty subset of ℝ n . A point x* ∈ C is a global solution, or more simply a solution to this problem, or a minimizer of f on C, if f(x*) ≤ f(x), ∀x ∈ C. We say that x* is a local solution to this problem if there exists a relatively
Cuong Le Van, Monique Florenzano
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Convex polytopes with convex nets

Mathematical Proceedings of the Cambridge Philosophical Society, 1975
The idea of anetwill be familiar to anyone who has made a model of a three-dimensional convex polytope (3-polytope) out of a flat sheet of card or similar material. To begin with, one cuts out a polygon, and then the model is formed by folding this and joining its edges in an appropriate manner. For example, Fig.
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Convex Optimization

IEEE Transactions on Automatic Control, 2004
Stephen P. Boyd, L. Vandenberghe
semanticscholar   +1 more source

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 Interpolation of Convex Data

1977
Abstract : This report contains the mathematical basis of an interpolation technique that constructs a smooth convex interpolant, called an H-Spline, for convex data on the real line. It is shown that an H-Spline always exists and is unique.
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A First-Order Primal-Dual Algorithm for Convex Problems with Applications to Imaging

Journal of Mathematical Imaging and Vision, 2011
A. Chambolle, T. Pock
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