Convex analysis

Convex analysis is the branch of mathematics devoted to the study of properties of convex functions and convex sets, often with applications in convex minimization, a subdomain of optimization theory.

See also

• List of convexity topics

References

• J.-B. Hiriart-Urruty; C. Lemaréchal (2001). Fundamentals of convex analysis. Berlin: Springer-Verlag. ISBN 978-3-540-42205-1. 
• Rockafellar, R. Tyrrell (1997) [1970]. Convex Analysis. Princeton, NJ: Princeton University Press. ISBN 9780691015866. 
• Singer, Ivan (1997). Abstract convex analysis. Canadian Mathematical Society series of monographs and advanced texts. New York: John Wiley & Sons, Inc.. pp. xxii+491. ISBN 0-471-16015-6. MR1461544. 
• Stoer, J.; Witzgall, C. (1970). Convexity and optimization in finite dimensions. 1. Berlin: Springer. ISBN 978-0387048352. 
• Zălinescu, C.. Convex analysis in general vector spaces. World Scientific Publishing  Co., Inc. pp. xx+367. ISBN 981-238-067-1. MR1921556. 

This mathematical analysis–related article is a stub. You can help Wikipedia by expanding it.v · Categories: Convex analysis Mathematical optimization Variational analysis Mathematical analysis stubs Wikimedia Foundation. 2010. Игры ⚽ Нужен реферат? Bare-eared Squirrel Monkey Black-capped Squirrel Monkey Look at other dictionaries: Characteristic function (convex analysis) — In the field of mathematics known as convex analysis, the characteristic function of a set is a convex function that indicates the membership (or non membership) of a given element in that set. It is similar to the usual indicator function, and… …   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 function — on an interval. A function (in black) is convex if and only i …   Wikipedia Convex geometry — is the branch of geometry studying convex sets, mainly in Euclidean space. Convex sets occur naturally in many areas of mathematics: computational geometry, convex analysis, discrete geometry, functional analysis, geometry of numbers, integral… …   Wikipedia Convex set — A convex set …   Wikipedia Convex cone — In linear algebra, a convex cone is a subset of a vector space over an ordered field that is closed under linear combinations with positive coefficients. A convex cone (light blue). Inside of it, the light red convex cone consists of all points… …   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 Convex hull — The convex hull of the red set is the blue convex set. See also: Convex set and Convex combination In mathematics, the convex hull or convex envelope for a set of points X in a real vector space V is the min …   Wikipedia Convex combination — Given three points x1,x2,x3 in a plane as shown in the figure, the point P is a convex combination of the three points, while Q is not. (Q is however an affine combination of the three poin …   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 18+ © Academic, 2000-2024 Contact us: Technical Support, Advertising Dictionaries export, created on PHP, Joomla, Drupal, WordPress, MODx. Mark and share Search through all dictionaries Translate… Search Internet Share the article and excerpts Direct link … Do a right-click on the link above and select “Copy Link”