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In geometry, set whose intersection with every line is a single line segment
geometry, a set of points is convex if it contains every line segment between two points in the set. For example, a solid cube is a convex set, but anything
Convex_set
Mathematical set with an ordering
convex sets of geometry, one uses order-convex instead of "convex". A convex sublattice of a lattice L is a sublattice of L that is also a convex set
Partially_ordered_set
Smallest convex set containing a given set
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
Convex_hull
Real function with secant line between points above the graph itself
function is convex if its epigraph (the set of points on or above the graph of the function) is a convex set. In simple terms, a convex function graph
Convex_function
Subfield of mathematical optimization
Convex optimization is a subfield of mathematical optimization that studies the problem of minimizing convex functions over convex sets (or, equivalently
Convex_optimization
Mathematics of convex functions and sets
Convex analysis is the branch of mathematics that studies convex sets, convex functions, and their applications to optimization, functional analysis,
Convex_analysis
Mathematical set closed under positive linear combinations
combinations with positive coefficients. It follows that convex cones are convex sets. The definition of a convex cone makes sense in a vector space over any ordered
Convex_cone
Property of point sets in Euclidean spaces
a set S {\displaystyle S} in the Euclidean space R n {\displaystyle \mathbb {R} ^{n}} is called a star domain (or star-convex set, star-shaped set or
Star_domain
Convex hull of a finite set of points in a Euclidean space
A convex polytope is a special case of a polytope, having the additional property that it is also a convex set contained in the n {\displaystyle n} -dimensional
Convex_polytope
problems in mathematical programming can be formulated as problems on convex sets or convex bodies. Six kinds of problems are particularly important: optimization
Algorithmic problems on convex sets
Algorithmic_problems_on_convex_sets
Polygon that is the boundary of a convex set
In geometry, a convex polygon is a polygon that is the boundary of a convex set. This means that the line segment between two points of the polygon is
Convex_polygon
Type of plane curve
Examples of convex curves include the convex polygons, the boundaries of convex sets, and the graphs of convex functions. Important subclasses of convex curves
Convex_curve
Convex and balanced set
disk. The disked hull or the absolute convex hull of a set is the intersection of all disks containing that set. A subset S {\displaystyle S} of a real
Absolutely_convex_set
convex sets (POCS), sometimes known as the alternating projection method, is a method to find a point in the intersection of two closed convex sets.
Projections_onto_convex_sets
Minimal superset that intersects each axis-parallel line in an interval
In geometry, a set K ⊂ Rd is defined to be orthogonally convex if, for every line L that is parallel to one of standard basis vectors, the intersection
Orthogonal_convex_hull
Type of mathematical functions
logarithmically convex. A Reinhardt domain D is called logarithmically convex if the image λ ( D ∗ ) {\displaystyle \lambda (D^{*})} of the set D ∗ = { z =
Function of several complex variables
Function_of_several_complex_variables
Space with topology generated by convex sets
whose topology is generated by translations of balanced, absorbent, convex sets. Alternatively they can be defined as a vector space with a family of
Locally convex topological vector space
Locally_convex_topological_vector_space
Branch of geometry
In mathematics, convex geometry is the branch of geometry studying convex sets, mainly in Euclidean space. Convex sets occur naturally in many areas: computational
Convex_geometry
All numbers between two given numbers
of the intervals. The concepts of convex sets and convex components are used in a proof that every totally ordered set endowed with the order topology is
Interval_(mathematics)
Linear combination of points where all coefficients are non-negative and sum to 1
In convex geometry and vector algebra, a convex combination is a linear combination of points (which can be vectors, scalars, or more generally points
Convex_combination
An integrally convex set is the discrete geometry analogue of the concept of convex set in geometry. A subset X of the integer grid Z n {\displaystyle
Integrally_convex_set
Form of projection
used to solve non-differentiable convex optimization problems. Many interesting problems can be formulated as convex optimization problems of the form
Proximal_gradient_method
Shape with seven sides
double lattice packing density of any convex set, and more generally for the optimal packing density of any convex set. Some 1000-kwacha coins from Zambia
Heptagon
Points with no three in a line
spaces as well as from compact convex co-convex subsets of a convex set. An example of cap sets comes from the card game Set, a card game in which each card
Cap_set
Sum of terms, each multiplied with a scalar
convex cones, and convex sets are generalizations of vector subspaces: a vector subspace is also an affine subspace, a convex cone, and a convex set,
Linear_combination
Topics referred to by the same term
joins points Convex polygon, a polygon which encloses a convex set of points Convex polytope, a polytope with a convex set of points Convex metric space
Convex
Non-empty convex set in Euclidean space
mathematics, a convex body in n {\displaystyle n} -dimensional Euclidean space R n {\displaystyle \mathbb {R} ^{n}} is a compact convex set with non-empty
Convex_body
Sequences of convex sets in a bounded set have convergent subsequences
topology and convex geometry about sequences of convex sets. Specifically, given a sequence { K n } {\displaystyle \{K_{n}\}} of convex sets contained in
Blaschke_selection_theorem
Topics referred to by the same term
enclosing a strictly convex set of points Strictly convex set, a set whose interior contains the line between any two points Strictly convex space, a normed
Strictly_convex
dimensions—are convex metric spaces. Given any two distinct points x {\displaystyle x} and y {\displaystyle y} in such a space, the set of all points z
Convex_metric_space
Mathematical function with convex lower level sets
a convex subset of a real vector space, such that for any real number y, the set of points on which the function value is at most y is a convex set. In
Quasiconvex_function
computational geometry, a set of points in the Euclidean plane or a higher-dimensional Euclidean space is said to be in convex position or convex independent if
Convex_position
Point not between two other points
In mathematics, an extreme point of a convex set S {\displaystyle S} in a real or complex vector space or affine space is a point in S {\displaystyle S}
Extreme_point
Shape that blocks all lines of sight
opaque set for the square, and for most other shapes this problem similarly remains unsolved. The shortest opaque set for any bounded convex set in the
Opaque_set
Sums vector sets A and B by adding each vector in A to each vector in B
the Minkowski sum with a vector subtraction. If the two convex shapes intersect, the resulting set will contain the origin. A − B = { a − b | a ∈ A , b
Minkowski_addition
Class of algorithms in computational geometry
proposed for computing the convex hull of a finite set of points, with various computational complexities. Computing the convex hull means that a non-ambiguous
Convex_hull_algorithms
Algorithms for solving convex optimization problems
convex function and G is a convex set. Without loss of generality, we can assume that the objective f is a linear function. Usually, the convex set G
Interior-point_method
(1969) for a full treatment of this problem. When the set A {\displaystyle A} is a convex set, the lim-inf above is a true limit, and one can show that
Minkowski–Steiner_formula
Planar surface that forms part of the boundary of a solid object
According to this definition, the set of faces of a polytope includes the polytope itself and the empty set. For convex polytopes, this definition is equivalent
Face_(geometry)
mathematics, a convex space (or barycentric algebra) is a space in which it is possible to take convex combinations of any finite set of points. A convex space
Convex_space
Set that can be "inflated" to reach any point
set – Convex and balanced set Balanced set – Construct in functional analysis Bornivorous set – Set that can absorb any bounded subset Bounded set (topological
Absorbing_set
Construct in functional analysis
origin and every convex neighborhood of the origin contains a balanced convex neighborhood of the origin (even if the TVS is not locally convex). This neighborhood
Balanced_set
Sets whose elements have degrees of membership
fuzzy set A ( U ⊆ R ) {\displaystyle A(U\subseteq \mathbb {R} )} is said to be convex (in the fuzzy sense, not to be confused with a crisp convex set), iff
Fuzzy_set
Problem in geometric probability
) Among continuous uniform distributions over bounded convex sets the probability of a convex quadrilateral is maximized by any circle or ellipse (probability
Sylvester's four point problem
Sylvester's_four_point_problem
Distance from origin of tangent hyperplanes
In mathematics, the support function hA of a non-empty closed convex set A in R n {\displaystyle \mathbb {R} ^{n}} describes the (signed) distances of
Support_function
is compact), but it is most useful for convex bodies (that is bodies, whose corresponding set is a convex set). The mean width of a line segment L is
Mean_width
Black-box description of a convex set
oracle) is a concept in the mathematical theory of convex optimization. It is a method to describe a convex set that is given as an input to an optimization
Separation_oracle
Subset of all points that is bounded by some given point of a dual (in a dual pairing)
functional and convex analysis, and related disciplines of mathematics, the polar set A ∘ {\displaystyle A^{\circ }} is a special convex set associated to
Polar_set
In mathematics, particularly in functional analysis and convex analysis, a convex series is a series of the form ∑ i = 1 ∞ r i x i {\displaystyle \sum
Convex_series
Every symmetric convex set in R^n with volume > 2^n contains a non-zero integer point
In mathematics, Minkowski's theorem is the statement that every convex set in R n {\displaystyle \mathbb {R} ^{n}} which is symmetric with respect to the
Minkowski's_theorem
Set of probability measures
measures. A credal set is often assumed or constructed to be a closed convex set. It is intended to express uncertainty or doubt about the probability
Credal_set
Infinite sum of monomials
region, is a convex set. More generally, one can show that when c=0, the interior of the region of absolute convergence is always a log-convex set in this
Power_series
Periodic set of points
\mathrm {d} (\Lambda )} , or more generally the volume of a symmetric convex set S {\displaystyle S} , to the number of lattice points contained in S
Lattice_(group)
Point in the convex hull of a set P in Rd, is the convex combination of d+1 points in P
in convex geometry. It states that if a point x {\displaystyle x} lies in the convex hull C o n v ( P ) {\displaystyle \mathrm {Conv} (P)} of a set P ⊂
Carathéodory's theorem (convex hull)
Carathéodory's_theorem_(convex_hull)
High-area shapes can shift to hold many grid points
states that any convex set in the plane that is centrally symmetric around the origin, with area greater than four (or a compact symmetric set with area equal
Blichfeldt's_theorem
geometry and computational geometry, the relative convex hull or geodesic convex hull is an analogue of the convex hull for the points inside a simple polygon
Relative_convex_hull
Geometric shape
self-intersecting torus). The lemon forms the boundary of a convex set, while its surrounding apple is non-convex. The ball in North American football has a shape
Lemon_(geometry)
On least area of curves of constant width
who published it separately in the early 20th century. The width of a convex set K {\displaystyle K} in the Euclidean plane is defined as the minimum distance
Blaschke–Lebesgue_theorem
Vector space with a notion of nearness
intersection of any family of convex sets is convex and the convex hull of a subset is equal to the intersection of all convex sets that contain it. Properties
Topological_vector_space
Hyperplane in geometry
the hyperplane. This theorem states that if S {\displaystyle S} is a convex set in the topological vector space X = R n , {\displaystyle X=\mathbb {R}
Supporting_hyperplane
Type of vector space in math
things named after David Hilbert Locally convex topological vector space – Space with topology generated by convex sets Operator topologies – Topologies on
Hilbert_space
Shape with same width in all directions
circles centered on a partial curve. Every body of constant width is a convex set, its boundary crossed at most twice by any line, and if the line crosses
Curve_of_constant_width
Generalization of topological interior
general sets. They are equal if both S 1 , S 2 {\displaystyle S_{1},S_{2}} are also convex. If S 1 , S 2 {\displaystyle S_{1},S_{2}} are convex and relatively
Relative_interior
Generalization of the concept of a norm
Different convex sets yield different seminorms, and every asymmetric seminorm on R n {\displaystyle \mathbb {R} ^{n}} can be obtained from some convex set, called
Asymmetric_norm
approximately Euclidean. Equivalently, every high-dimensional bounded symmetric convex set has low-dimensional sections that are approximately ellipsoids. A new
Dvoretzky's_theorem
Haar null set Convex set Balanced set, Absolutely convex set Fractal set Recursive set Recursively enumerable set Arithmetical set Diophantine set Hyperarithmetical
List_of_types_of_sets
Shape containing unit line segments in all directions
360°. This question was first posed, for convex regions, by Sōichi Kakeya (1917). The minimum area for convex sets is achieved by an equilateral triangle
Kakeya_set
Space formed by the ''n''-tuples of real numbers
define a convex cone, which contains all non-negative linear combinations of its vectors. Corresponding concept in an affine space is a convex set, which
Real_coordinate_space
Normed vector space for which the closed unit ball is strictly convex
strictly convex space is a normed vector space (X, || ||) for which the closed unit ball is a strictly convex set. Put another way, a strictly convex space
Strictly_convex_space
Violations of the convexity assumptions of elementary economics
convex preferences (that do not prefer extremes to in-between values) and convex budget sets and on producers with convex production sets; for convex
Non-convexity_(economics)
On when a space equals the closed convex hull of its extreme points
compact convex sets in locally convex topological vector spaces (TVSs). Krein–Milman theorem—A compact convex subset of a Hausdorff locally convex topological
Krein–Milman_theorem
Theorems generalizing the Brouwer fixed-point theorem
fixed-point theorem: Let V be a locally convex topological vector space. For any nonempty compact convex set X in V, any continuous function f : X → X
Fixed-point theorems in infinite-dimensional spaces
Fixed-point_theorems_in_infinite-dimensional_spaces
is: If K is any bounded convex set in the n-dimensional Euclidean space Rn, then there exists a set of 2n scalars si and a set of 2n translation vectors
Hadwiger conjecture (combinatorial geometry)
Hadwiger_conjecture_(combinatorial_geometry)
Type of function in linear algebra
: X → R {\displaystyle p\colon X\to \mathbb {R} } which is subadditive, convex, and satisfies p ( 0 ) ≤ 0 {\displaystyle p(0)\leq 0} is also positively
Sublinear_function
Largest distance between two points
Euclidean space, the diameter of the object or set is the same as the diameter of its convex hull. For any convex shape in the plane, the diameter is the largest
Diameter_of_a_set
Curved triangle with constant width
1215/ijm/1256051608, MR 0320885. Hernández Cifre, M. A. (2000), "Is there a planar convex set with given width, diameter, and inradius?", American Mathematical Monthly
Reuleaux_triangle
Convex continuous functions on compact convex sets maximize at extreme points
function that is convex and continuous, and defined on a set that is convex and compact, attains its maximum at some extreme point of that set. It is attributed
Bauer_maximum_principle
Significant topic in economics
the intersection of two convex sets is a convex set. More generally, the intersection of a family of convex sets is a convex set. For every subset Q of
Convexity_in_economics
fixed-point theorems often require a convex set. The analogue of this property for discrete sets is an integrally-convex set. A fixed point of a discrete function
Discrete_fixed-point_theorem
commuting family of continuous affine self-mappings of a compact convex subset in a locally convex topological vector space has a common fixed point. This theorem
Markov–Kakutani fixed-point theorem
Markov–Kakutani_fixed-point_theorem
Concept in economics
preference relation ⪰ {\displaystyle \succeq } on the consumption set X is called convex if whenever x , y , z ∈ X {\displaystyle x,y,z\in X} where y ⪰ x
Convex_preferences
Correspondence in functional analysis
\{0\}} . Theorem—The set of states of a C ∗ {\displaystyle C^{*}} -algebra A {\displaystyle A} with a unit element is a compact convex set under the weak-
Gelfand–Naimark–Segal construction
Gelfand–Naimark–Segal_construction
Type of topological space
e>0} must go outside the cube in some dimension. The Hilbert cube is a convex set, whose span is dense in the whole space, but whose interior is empty.
Hilbert_cube
Optimization algorithm
the intersection of convex sets, and is a variant of the alternating projection method (also called the projections onto convex sets method). In its simplest
Dykstra's projection algorithm
Dykstra's_projection_algorithm
On the existence of hyperplanes separating disjoint convex sets
disjoint convex sets in n-dimensional Euclidean space. There are several rather similar versions. In one version of the theorem, if both these sets are closed
Hyperplane_separation_theorem
Inequality which involves a linear function
inequalities. It is a convex set, since the half-spaces are convex sets, and the intersection of a set of convex sets is also convex. In the non-degenerate
Linear_inequality
A convex cap is a well defined structure in mathematics commonly used in convex geometry for approximating convex shapes. It is used in the construction
Convex_cap
Measure of difference between two points
\mathbb {R} } be a continuously-differentiable, strictly convex function defined on a convex set Ω {\displaystyle \Omega } . The Bregman distance associated
Bregman_divergence
Set of points touching all convex bodies of unit volume
set of points that touches every convex body of unit volume. Ludwig Danzer asked whether it is possible for such a set to have bounded density. Several
Danzer_set
Cone of outward normals to a convex set at a point
In convex analysis and optimization, the normal cone to a set at a point is a convex cone consisting of vectors that make a non-acute angle with every
Normal_cone_(convex_analysis)
Theorem about the intersections of d-dimensional convex sets
theorem is a basic result in discrete geometry on the intersection of convex sets. It was discovered by Eduard Helly in 1913, but not published by him
Helly's_theorem
Shape that can be represented as a linear matrix inequality
In convex geometry, a spectrahedron is a shape that can be represented as a linear matrix inequality. Alternatively, the set of n × n positive semidefinite
Spectrahedron
Sums of sets of vectors are nearly convex
The Shapley–Folkman lemma is a result in convex geometry that describes the Minkowski addition of sets in a vector space. The lemma may be intuitively
Shapley–Folkman_lemma
Type of mathematical function
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
Logarithmically concave function
Logarithmically_concave_function
be a Riemannian manifold. A subset C of M is said to be a geodesically convex set if, given any two points in C, there is a unique minimizing geodesic contained
Geodesic_convexity
Color reproduction capability
reproduction and colorimetry, a gamut, or color gamut /ˈɡæmət/, is a convex set containing the colors that can be accurately represented, i.e. reproduced
Gamut
Iterative method for minimizing convex functions
the ellipsoid method is an iterative method for minimizing convex functions over convex sets. The ellipsoid method generates a sequence of ellipsoids whose
Ellipsoid_method
self-concordant function, that is also a barrier function for a particular convex set. Self-concordant barriers are important ingredients in interior point
Self-concordant_function
Generalization of the Legendre transformation
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_conjugate
Distance function
distance in the Cayley–Klein model of hyperbolic geometry, where the convex set is the n-dimensional open unit ball. Hilbert's metric has been applied
Hilbert_metric
CONVEX SET
CONVEX SET
Boy/Male
Irish American
Hound lover. Full of desire; much desire.
Surname or Lastname
English
English : habitational name from a place named Cove, examples of which are found in Devon, Hampshire, and Suffolk, from Old English cofa ‘cove’, ‘bay’, ‘inlet’, also ‘shelter’, ‘hut’, or a topographic name with the same meaning.
Boy/Male
British, Christian, English
Wagoner; To Convey
Surname or Lastname
English
English : metathesized form of the occupational name Coyner.English : possibly an occupational name for a dealer in rabbits or rabbit skins, from an agent derivative of Middle English cony ‘rabbit’ (see Coney).
Boy/Male
American, British, English
Shepherd
Surname or Lastname
Spanish and Portuguese
Spanish and Portuguese : nickname from the title of rank conde ‘count’, a derivative of Latin comes, comitis ‘companion’.English : unexplained.
Boy/Male
Irish
Hero.
Surname or Lastname
Irish
Irish : variant spelling of Connor, now common in Scotland.English : occupational name for an inspector of weights and measures, Middle English connere, cunnere ‘inspector’, an agent derivative of cun(nen) ‘to examine’.
Male
English
Anglicized form of Irish Gaelic Conláed, CONLEY means "purifying fire."
Boy/Male
Indian, Kannada, Tamil
God Murugan
Boy/Male
Irish American
Strong willed or wise. Also a : Hero.
Male
English
Variant spelling of English Connor, CONNER means "hound-lover."
Surname or Lastname
English (Leicestershire)
English (Leicestershire) : variant of Culver.
Boy/Male
American, British, English
Dove
Surname or Lastname
English
English : from Middle English cony ‘rabbit’ (a back-formation from conies, from Old French conis, plural of conil), a nickname for someone thought to resemble a rabbit in some way or a metonymic occupational name for a dealer in rabbits or rabbit skins.
Surname or Lastname
English
English : from Old French covine ‘fraud’, ‘deceit’, hence a derogatory nickname for a trickster.English : habitational name from a place in Staffordshire named Coven ‘(place) at the huts or shelters (Old English cofa, dative plural cofum)’.
Boy/Male
American, Christian, German, Indian
High Desire
Surname or Lastname
English
English : unexplained.
Boy/Male
Irish
Hound of the plains.
Surname or Lastname
Italian
Italian : from the title of rank conte ‘count’ (from Latin comes, genitive comitis ‘companion’). Probably in this sense (and the Late Latin sense of ‘traveling companion’), it was a medieval personal name; as a title it was no doubt applied ironically as a nickname for someone with airs and graces or simply for someone who worked in the service of a count.English : variant of Count, cognate with 1.French : nickname for someone in the service of a count or for someone who behaved pretentiously, from Old French conte, cunte ‘count’ (of the same derivation as 1).French (Conté) : variant of Comté (see Comte).
CONVEX SET
CONVEX SET
Boy/Male
Tamil
Variant of Jaydev (God has heard
Surname or Lastname
English
English : variant of Dominey.
Boy/Male
German
The Brother Names
Male
English
Anglicized form of Hebrew Machliy, MAHALI means "sick." In the bible, this is the name of a son of Merari. Also spelled Mahli.
Male
Chinese
dragon greatness.
Female
Hawaiian
Hawaiian name KANI means "sound."
Girl/Female
Indian, Punjabi, Sikh
Dawn
Girl/Female
Indian
Lord rams devotees, Daughter of cyprus (Daughter of cyprus)
Girl/Female
Australian, Greek
Birth Mark; Blemish
Girl/Female
Tamil
Tender
CONVEX SET
CONVEX SET
CONVEX SET
CONVEX SET
CONVEX SET
a.
Convex on both sides; as, a biconvex lens.
imp. & p. p.
of Cove
v. t.
To impart or communicate; as, to convey an impression; to convey information.
dv.
In a convex form; convexly.
n. & v.
See Conge, Conge.
v. t.
To context.
a.
Convex on both sides; double convex. See under Convex, a.
v. t.
To exchange for some specified equivalent; as, to convert goods into money.
v. t.
To cause to pass from one place or person to another; to serve as a medium in carrying (anything) from one place or person to another; to transmit; as, air conveys sound; words convey ideas.
a.
Plane or flat on one side, and convex on the other; as, a plano-convex lens. See Convex, and Lens.
a.
Specifically, having such a combination of concave and convex sides as makes the focal axis the shortest line between them. See Illust. under Lens.
adv.
In a convex form; as, a body convexly shaped.
a.
Convex on one side, and concave on the other. The curves of the convex and concave sides may be alike or may be different. See Meniscus.
a.
Made convex; protuberant in a spherical form.
n.
The conger eel; -- called also congeree.
n.
A convex body or surface.
a.
Convex on one side, and flat on the other; plano-convex.
v. t.
To call before a judge or judicature; to summon; to convene.
v. t.
To accompany; to convoy.
a.
Concave on one side and convex on the other, as an eggshell or a crescent.