Convex analysis information

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

nonnegative matrix is a convex function of its diagonal elements. Concave function Convex analysis Convex conjugate Convex curve Convex optimization Geodesic...

devoted to the study of properties of convex sets and convex functions is called convex analysis. The notion of a convex set can be generalized as described...

mathematical optimization, the convex conjugate of a function is a generalization of the Legendre transformation which applies to non-convex functions. It is also...

Convex optimization is a subfield of mathematical optimization that studies the problem of minimizing convex functions over convex sets (or, equivalently...

In geometry, the convex hull, convex envelope or convex closure of a shape is the smallest convex set that contains it. The convex hull may be defined...

linear combinations with positive coefficients. It follows that convex cones are convex sets. In this article, only the case of scalars in an ordered field...

In functional analysis and related areas of mathematics, locally convex topological vector spaces (LCTVS) or locally convex spaces are examples of topological...

mathematical analysis, in particular the subfields of convex analysis and optimization, a proper convex function is an extended real-valued convex function...

Carl Friedrich Gauss (1777–1855) is the eponym of all of the topics listed below. There are over 100 topics all named after this German mathematician and...

naturally in many areas: computational geometry, convex analysis, discrete geometry, functional analysis, geometry of numbers, integral geometry, linear...

In convex geometry and vector algebra, a convex combination is a linear combination of points (which can be vectors, scalars, or more generally points...

(2004). Convex optimization (PDF). New York: Cambridge. pp. 639–640. ISBN 978-0521833783. Rockafellar, R. Tyrrell (1997) [1970]. Convex Analysis. Princeton...

function is the convex conjugate of the cost function. Convex analysis is the standard tool for analyzing textbook economics. Non‑convex phenomena in economics...

augmented Lagrangian algorithm for solving convex quadratic optimization problems" (PDF). Journal of Convex Analysis. 12: 45–69. Archived (PDF) from the original...

on a convex subset of a real vector space such that the inverse image of any set of the form ( − ∞ , a ) {\displaystyle (-\infty ,a)} is a convex set....

Dual cone and polar cone are closely related concepts in convex analysis, a branch of mathematics. The dual cone C* of a subset C in a linear space X...

In mathematics, variational analysis is the combination and extension of methods from convex optimization and the classical calculus of variations to a...

a theorem in functional analysis that characterizes the bipolar (that is, the polar of the polar) of a set. In convex analysis, the bipolar theorem refers...

of a real or complex vector space is said to be absolutely convex or disked if it is convex and balanced (some people use the term "circled" instead of...

processes. Set-valued analysis – applies ideas from analysis and topology to set-valued functions. Convex analysis, the study of convex sets and functions...

is one for which the value at any convex combination of elements in the domain is greater than or equal to the convex combination of the values at the...

In convex analysis, a non-negative function f : Rn → R+ is logarithmically concave (or log-concave for short) if its domain is a convex set, and if it...

1080/02331930412331327157. S2CID 219698493. Bauschke, Heinz H. (2017). Convex Analysis and Monotone Operator Theory in Hilbert Spaces. New York: Springer...

El Ghaoui, Laurent (2017). Optimization Models and Applications. "convex analysis - About the strictly convexity of log-sum-exp function - Mathematics...