strictly convex

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• Strictly convex space — In mathematics, a strictly convex space is a normed topological vector space ( V , || ||) for which the unit ball is a strictly convex set. Put another way, a strictly convex space is one for which, given any two points x and y in the boundary ∂… …   Wikipedia

• Convex function — on an interval. A function (in black) is convex if and only i …   Wikipedia

• Convex optimization — Convex minimization, a subfield of optimization, studies the problem of minimizing convex functions over convex sets. Given a real vector space X together with a convex, real valued function defined on a convex subset of X, the problem is to find …   Wikipedia

• Convex and concave polygons — An example of a convex polygon: a regular pentagon In geometry, a polygon can be either convex or concave (non convex). Contents 1 Convex polygons …   Wikipedia

• Convex preferences — In economics, convex preferences refer to a property of an individual s ordering of various outcomes which roughly corresponds to the idea that averages are better than the extremes . The concept roughly corresponds to the law of diminishing… …   Wikipedia

• Convex conjugate — In mathematics, convex conjugation is a generalization of the Legendre transformation. It is also known as Legendre–Fenchel transformation or Fenchel transformation (after Adrien Marie Legendre and Werner Fenchel). Contents 1 Definition 2… …   Wikipedia

• Quasiconvex function — In mathematics, a quasiconvex function is a real valued function defined on an interval or on a convex subset of a real vector space such that the inverse image of any set of the form ( infty,a) is a convex set. Definition and… …   Wikipedia

• Jensen's inequality — In mathematics, Jensen s inequality, named after the Danish mathematician Johan Jensen, relates the value of a convex function of an integral to the integral of the convex function. It was proved by Jensen in 1906 [Jensen, J. Sur les fonctions… …   Wikipedia

• Legendre transformation — f(x) . The function is shown in red, and the tangent line at point (x 0, f(x 0)) is shown in blue. The tangent line intersects the vertical axis at (0, f^star) and f^star is the value of the Legendre transform f^star(p 0) , where p 0=dot{f}(x 0) …   Wikipedia

• Johnson solid — The elongated square gyrobicupola (J37), a Johnson solid …   Wikipedia

• Bregman divergence — In mathematics Bregman divergence or Bregman distance is similar to a metric, but does not satisfy the triangle inequality nor symmetry. There are two ways in which Bregman divergences are important. Firstly, they generalize squared Euclidean… …   Wikipedia