Convex analysis

subset of an affine space that is closed under convex combinations

real function with secant line between points above the graph itself

theorem of convex functions

notion in topological vector spaces

negative of a convex function

involutive transformation on real-valued convex functions of one real variable

property of point sets in Euclidean spaces

geometric relation between the roots of a polynomial and those of its derivative

the set of points lying on or above the graph of a function

subfield of mathematical optimization

branch of mathematics devoted to the study of properties of convex functions and convex sets

topological vector space in which every vector has a convex neighborhood

function made from a set

subset of a vector space closed under positive linear combinations

symmetric convex set

the ("dual") lower-semicontinuous convex function resulting from the Legendre–Fenchel transformation of a "primal" function

theorem

function for which every set of inputs whose value is below a given threshold is convex

concepts in convex analysis

geometric property of a pair of sets of points in Euclidean geometry

convex and balanced set

normed vector space for which the closed unit ball is strictly convex

reflexive Banach space such that the center of a line segment inside the unit ball must lie deep inside the unit ball unless the segment is short

Mathematical analysis term

theorem in convex analysis

Algebra theorem about convex functions

theorem

American mathematician

mathematical theorem in convex analysis

concept in convex analysis

terms in Maths

concept in convex optimization mathematics

on closed convex subsets in Hilbert space