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This is a list of convexity topics, by Wikipedia page. *Alpha blending - the process of combining a translucent foreground color with a background color, thereby producing a new blended color. This is a convex combination of two colors allowing for transparency effects in computer graphics. *Barycentric coordinates - a coordinate system in which the location of a point of a simplex (a triangle, tetrahedron, etc.) is specified as the center of mass, or barycenter, of masses placed at its vertices. The coordinates are non-negative for points in the convex hull. *Borsuk's conjecture - a conjecture about the number of pieces required to cover a body with a larger diameter. Solved by Hadwiger for the case of smooth convex bodies. *Bond convexity - a measure of the non-linear relationship between price and yield duration of a bond to changes in interest rates, the second derivative of the price of the bond with respect to interest rates. A basic form of convexity in finance. *Carathéodory's theorem (convex hull) - If a point ''x'' of ''R^d'' lies in the convex hull of a set ''P'', there is a subset of ''P'' with ''d''+1 or fewer points such that ''x'' lies in its convex hull. *Choquet theory - an area of functional analysis and convex analysis concerned with measures with support on the extreme points of a convex set ''C''. Roughly speaking, all vectors of ''C'' should appear as 'averages' of extreme points. *Complex convexity — extends the notion of convexity to complex numbers. *Convex analysis - the branch of mathematics devoted to the study of properties of convex functions and convex sets, often with applications in convex minimization. *Convex combination - a linear combination of points where all coefficients are non-negative and sum to 1. All convex combinations are within the convex hull of the given points. *Convex and concave - a print by Escher in which many of the structure's features can be seen as both convex shapes and concave impressions. *Convex body - a compact convex set in a Euclidean space whose interior is non-empty. *Convex conjugate - a dual of a real functional in a vector space. Can be interpreted as an encoding of the convex hull of the function's epigraph in terms of its supporting hyperplanes. *Convex curve - a curve that lies entirely on one side of each of its tangents. The interior of a convex curve is a convex set. *Convex function - a function in which the line segment between any two points on the graph of the function lies above the graph. * * *Closed convex function - a convex function whose every the sublevel set is a closed set. * * *Proper convex function - a convex function whose effective domain is nonempty and it never attains minus infinity. * * *Concave function - the negative of a convex function. *Convex geometry - the branch of geometry studying convex sets, mainly in Euclidean space. Contains three sub-branches: general convexity, polytopes and polyhedra, and discrete geometry. *Convex hull (aka ''convex envelope'') - the smallest convex set that contains a given set of points in Euclidean space. *Convex lens - a lens in which one or two sides is curved or bowed outwards. Light passing through the lens is converged (or focused) to a spot behind the lens. *Convex optimization - a subfield of optimization, studies the problem of minimizing convex functions over convex sets. The convexity property can make optimization in some sense "easier" than the general case - for example, any local minimum must be a global minimum. *Convex polygon - a 2-dimensional polygon whose interior is a convex set in the Euclidean plane. *Convex polytope - an ''n''-dimensional polytope which is also a convex set in the Euclidean ''n''-dimensional space. *Convex set - a set in Euclidean space in which contains every segment between every two of its points. *Convexity (finance) - refers to non-linearities in a financial model. When the price of an underlying variable changes, the price of an output does not change linearly, but depends on the higher-order derivatives of the modeling function. Geometrically, the model is no longer flat but curved, and the degree of curvature is called the convexity. *Epigraph (mathematics) *Extreme point *Fenchel conjugate *Fenchel's inequality *Fixed point theorems in infinite-dimensional spaces *Four vertex theorem - every convex curve has at least 4 vertices. *Gift wrapping algorithm *Graham scan *Hadwiger conjecture (combinatorial geometry) - any convex body in n-dimensional Euclidean space can be covered by 2^n or fewer smaller bodies homothetic with the original body. *Hadwiger's theorem - a theorem that characterizes the valuations on convex bodies in R^n. *Helly's theorem *Hyperplane *Indifference curve *Infimal convolute *Interval (mathematics) *Jarvis march *Jensen's inequality *Lagrange multiplier *Legendre transformation *Locally convex topological vector space *Mahler volume *Minkowski's theorem *Mixed volume *Mixture density *Newton polygon *Radon's theorem *Separating axis theorem *Shapley–Folkman lemma *Shephard's problem *Simplex *Simplex method *Subdifferential *Supporting hyperplane *Supporting hyperplane theorem 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「List of convexity topics」の詳細全文を読む スポンサード リンク
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