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Topics referred to by the same term
Look up convex or convexity in Wiktionary, the free dictionary. Convex or convexity may refer to: Convex lens, in optics Convex set, containing the whole
Convex
In geometry, set whose intersection with every line is a single line segment
crescent shape, is not convex. The boundary of a convex set in the plane is always a convex curve. The intersection of all the convex sets that contain a
Convex_set
Real function with secant line between points above the graph itself
In mathematics, a real-valued function is called convex if the line segment between any two distinct points on the graph of the function lies above or
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
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
Flat-sided three-dimensional shape
reflecting. Convex polyhedra are a well-defined class of polyhedra with several equivalent standard definitions. Every convex polyhedron is the convex hull of
Polyhedron
Optical device which transmits and refracts light
the Latin name of the lentil (a seed of a lentil plant), because a double-convex lens is lentil-shaped. The lentil also gives its name to a geometric figure
Lens
In geometry, a convex polyhedron whose faces are regular polygons is known as a Johnson solid, or sometimes as a Johnson–Zalgaller solid. Some authors
List_of_Johnson_solids
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
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
Euclidean space is said to be in convex position or convex independent if none of the points can be represented as a convex combination of the others. A finite
Convex_position
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
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
Any of the five regular polyhedra
In geometry, a Platonic solid is a convex, regular polyhedron in three-dimensional Euclidean space. Being a regular polyhedron means that the faces are
Platonic_solid
Topics referred to by the same term
Strictly convex may refer to: Strictly convex function, a function having the line between any two points above its graph Strictly convex polygon, a polygon
Strictly_convex
Class of algorithms in computational geometry
Algorithms that construct convex hulls of various objects have a broad range of applications in mathematics and computer science. In computational geometry
Convex_hull_algorithms
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
Topics referred to by the same term
Look up plano-convex in Wiktionary, the free dictionary. Plano-convex may refer to: Plano-convex lens, in optics Plano-convex, a type of mudbrick used
Plano-convex
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
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
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
Topics referred to by the same term
in a Convex Mirror may refer to: Self-Portrait in a Convex Mirror (Parmigianino), a c. 1524 painting by Parmigianino Self-Portrait in a Convex Mirror
Self-Portrait in a Convex Mirror
Self-Portrait_in_a_Convex_Mirror
Function whose composition with the logarithm is convex
logarithmically convex or superconvex if log ∘ f {\displaystyle {\log }\circ f} , the composition of the logarithm with f, is itself a convex function. Let
Logarithmically convex function
Logarithmically_convex_function
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:
Convex_geometry
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
Concept in economics
In economics, convex preferences are an individual's ordering of various outcomes, typically with regard to the amounts of various goods consumed, with
Convex_preferences
Plane figure bounded by line segments
boundary of the polygon does not cross itself. All convex polygons are simple. Concave: Non-convex and simple. There is at least one interior angle greater
Polygon
Class of 4-dimensional polytopes
non-prismatic convex uniform 4-polytopes. There are two infinite sets of convex prismatic forms, along with 17 cases arising as prisms of the convex uniform
Uniform_4-polytope
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
Function in mathematical analysis
In mathematics, a Schur-convex function, also known as S-convex, isotonic function and order-preserving function is a function f : R d → R {\displaystyle
Schur-convex_function
Space with topology generated by convex sets
analysis and related areas of mathematics, locally convex topological vector spaces (LCTVS) or locally convex spaces are examples of topological vector spaces
Locally convex topological vector space
Locally_convex_topological_vector_space
American computer manufacturer
Convex Computer Corporation was a company that developed, manufactured and marketed vector minisupercomputers and supercomputers for small-to-medium-sized
Convex_Computer
The dynamic convex hull problem is a class of dynamic problems in computational geometry. The problem consists in the maintenance, i.e., keeping track
Dynamic_convex_hull
Polyhedron with 20 faces
(convex, non-stellated) regular icosahedron—one of the Platonic solids—whose faces are 20 equilateral triangles. There are two objects, one convex and
Icosahedron
Convex polyhedron with regular faces
Johnson solid, sometimes also known as a Johnson–Zalgaller solid, is a convex polyhedron whose faces are regular polygons and that is not a uniform polyhedron
Johnson_solid
Two-sided graph with consecutive neighbors
In the mathematical field of graph theory, a convex bipartite graph is a bipartite graph with specific properties. A bipartite graph ( U ∪ V , E ) {\displaystyle
Convex_bipartite_graph
authors have studied the computation of the volume of high-dimensional convex bodies, a problem that can also be used to model many other problems in
Convex_volume_approximation
of "convexity" on metric spaces. Karl Menger defined a metric space as convex if any "segment" joining two points in that space has other points in it
Convex_metric_space
Mirror with a curved reflecting surface
is a mirror with a curved reflecting surface. The surface may be either convex (bulging outward) or concave (recessed inward). Most curved mirrors have
Curved_mirror
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
Mathematical set with an ordering
with 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
rotational symmetry. Uniform polyhedra can be divided between convex forms with convex regular polygon faces and star forms. Star forms have either regular
List_of_uniform_polyhedra
Four-sided polygon
complex (self-intersecting, or crossed). Simple quadrilaterals are either convex or concave. The interior angles of a simple (and planar) quadrilateral ABCD
Quadrilateral
Polyhedron made of equilateral triangles
convexity. The simplest convex deltahedron is the regular tetrahedron, a pyramid with four equilateral triangles. There are eight convex deltahedra, which can
Deltahedron
Terms in Maths
This definition is valid for any function, but most used for convex functions. A proper convex function is closed if and only if it is lower semi-continuous
Closed_convex_function
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
Lithograph by Dutch artist M. C. Escher
Convex and Concave is a lithograph print by the Dutch artist M. C. Escher, first printed in March 1955. It depicts an ornate architectural structure with
Convex_and_Concave
Point in the convex hull of a set P in Rd, is the convex combination of d+1 points in P
Carathéodory's theorem is a theorem in convex geometry. It states that if a point x {\displaystyle x} lies in the convex hull C o n v ( P ) {\displaystyle
Carathéodory's theorem (convex hull)
Carathéodory's_theorem_(convex_hull)
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
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
Smallest convex polygon containing a given polygon
In discrete geometry and computational geometry, the convex hull of a simple polygon is the polygon of minimum perimeter that contains a given simple polygon
Convex hull of a simple polygon
Convex_hull_of_a_simple_polygon
In measure and probability theory in mathematics, a convex measure is a probability measure that — loosely put — does not assign more mass to any intermediate
Convex_measure
geodesically convex subset of M. A function f : C → R {\displaystyle f:C\to \mathbf {R} } is said to be a (strictly) geodesically convex function if the
Geodesic_convexity
Spatial tiling of convex uniform polyhedra
geometry, a convex uniform honeycomb is a uniform tessellation which fills three-dimensional Euclidean space with non-overlapping convex uniform polyhedral
Convex_uniform_honeycomb
Painting by George Washington Lambert
The Convex Mirror is a c 1916 oil with pencil on wood panel painting by Australian artist George Washington Lambert. The work depicts the interior of Belwethers
The_Convex_Mirror
In mathematics, an invariant convex cone is a closed convex cone in a Lie algebra of a connected Lie group that is invariant under inner automorphisms
Invariant_convex_cone
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
In geometric graph theory, a convex embedding of a graph is an embedding of the graph into a Euclidean space, with its vertices represented as points and
Convex_embedding
Four-dimensional analogue of the cube
cubical cells, meeting at right angles. The tesseract is one of the six convex regular 4-polytopes. The tesseract is also called an 8-cell, C8, (regular)
Tesseract
functional analysis, a locally convex vector lattice (LCVL) is a topological vector lattice that is also a locally convex space. LCVLs are important in
Locally_convex_vector_lattice
A kinetic convex hull data structure is a kinetic data structure that maintains the convex hull of a set of continuously moving points. It should be distinguished
Kinetic_convex_hull
Mathematical function with convex lower level sets
on 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
Quasiconvex_function
Mathematical function
K-convex functions, first introduced by Scarf, are a special weakening of the concept of convex function which is crucial in the proof of the optimality
K-convex_function
onto 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
Convex and balanced set
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
Absolutely_convex_set
Polyhedron with 6 faces
are seven topologically distinct convex hexahedra, one of which exists in two mirror image forms. Additional non-convex hexahedra exist, with their number
Hexahedron
Planar graph with convex polygon faces
In graph drawing, a convex drawing of a planar graph is a drawing that represents the vertices of the graph as points in the Euclidean plane and the edges
Convex_drawing
Concept in mathematics of vector spaces
In mathematics, uniformly convex spaces (or uniformly rotund spaces) are common examples of reflexive Banach spaces. The concept of uniform convexity was
Uniformly_convex_space
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
Plano-convex ingots are lumps of metal with a flat or slightly concave top and a convex base. They are sometimes, misleadingly, referred to as bun ingots
Plano-convex_ingot
Polyhedron with eight triangular faces
vertex. Many types of irregular octahedra also exist, including both convex and non-convex shapes. The regular octahedron has eight equilateral triangle sides
Octahedron
Topics referred to by the same term
In mathematics, a convex graph may be a convex bipartite graph a convex plane graph the graph of a convex function This disambiguation page lists articles
Convex_graph
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
Concept in convex analysis
particular the subfields of convex analysis and optimization, a proper convex function is an extended real-valued convex function with a non-empty domain
Proper_convex_function
Four-dimensional analogues of the regular polyhedra in three dimensions
polygons in two dimensions. There are six convex and ten star regular 4-polytopes, giving a total of sixteen. The convex regular 4-polytopes were first described
Regular_4-polytope
Graph that can be embedded in the plane
graph is said to be convex if all of its faces (including the outer face) are convex polygons. Not all planar graphs have a convex embedding (e.g. the
Planar_graph
Convex quadrilateral with at least one pair of parallel sides
usually considered to be a convex quadrilateral in Euclidean geometry, but there are also crossed cases. If shape ABCD is a convex trapezoid, then the ABDC
Trapezoid
Convex polyhedron with six faces with four edges each
faces. Etymologically, "cuboid" means "like a cube", in the sense of a convex solid which can be transformed into a cube (by adjusting the lengths of
Cuboid
Tiling of the plane by pentagons
that is topologically equivalent to the dodecahedron. Fifteen types of convex pentagons are known to tile the plane monohedrally (i.e., with one type
Pentagonal_tiling
1967 mathematics textbook
Convex Polytopes is a graduate-level mathematics textbook about convex polytopes, higher-dimensional generalizations of three-dimensional convex polyhedra
Convex_Polytopes
This table shows the 11 convex uniform tilings (regular and semiregular) of the Euclidean plane, and their dual tilings. There are three regular and eight
List of Euclidean uniform tilings
List_of_Euclidean_uniform_tilings
Covering by shapes without overlaps or gaps
shape is allowed. Polyominoes are examples of tiles that are either convex of non-convex, for which various combinations, rotations, and reflections can be
Tessellation
Study of mathematical algorithms for optimization problems
unless the objective function is convex in a minimization problem, there may be several local minima. In a convex problem, if there is a local minimum
Mathematical_optimization
Visual artifacts in ivory cross-sections
and convex angle. Concave angles have slightly concave sides and open to the medial (inner) area of the tusk. Convex angles have somewhat convex sides
Schreger_line
Theorem on extension of bounded linear functionals
theorem or the hyperplane separation theorem, and has numerous uses in convex geometry. The theorem is named for the mathematicians Hans Hahn and Stefan
Hahn–Banach_theorem
Theorem of convex functions
mathematician Johan Jensen, relates the value of a convex function of an integral to the integral of the convex function. It was proved by Jensen in 1906, building
Jensen's_inequality
In the field of mathematics known as convex analysis, the indicator function of a set is a convex function that indicates the membership (or non-membership)
Indicator function (convex analysis)
Indicator_function_(convex_analysis)
Algorithms for solving convex optimization problems
barrier methods or IPMs) are algorithms for solving linear and non-linear convex optimization problems. IPMs combine two advantages of previously-known algorithms:
Interior-point_method
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
Mathematics concept
In mathematics, the lower convex envelope f ˘ {\displaystyle {\breve {f}}} of a function f {\displaystyle f} defined on an interval [ a , b ] {\displaystyle
Lower_convex_envelope
Partial order on matrices
the convex cone of positive semi-definite matrices. This order is usually employed to generalize the definitions of monotone and concave/convex scalar
Loewner_order
peeling or convex skull problem is a problem of finding the convex polygon of the largest possible area that lies within a given non-convex simple polygon
Potato_peeling
Three-dimensional curved geometric object
geometric object that was discovered by Paul Schatz in 1929. It is the convex hull of a skeletal frame made by placing two linked congruent circles in
Oloid
Subdivision of the plane into polygons that are all regular
Tilings of the Euclidean plane by convex regular polygons have been widely used since antiquity. The first systematic mathematical treatment was that of
Euclidean tilings by convex regular polygons
Euclidean_tilings_by_convex_regular_polygons
Shape with three sides
either convex (bending outward) or concave (bending inward). The intersection of three disks forms a circular triangle whose sides are all convex. An example
Triangle
Five coplanar points have a subset forming a convex quadrilateral
or more points are vertices of the convex hull, any four such points can be chosen. If on the other hand, the convex hull has the form of a triangle with
Happy_ending_problem
Negative of a convex function
which the function value at any convex combination of elements in the domain is greater than or equal to that convex combination of those domain elements
Concave_function
Supplementary pair of angles at each vertex of a polygon
simple polygon (non-self-intersecting), regardless of whether it is convex or non-convex, this angle is called an internal angle (or interior angle) if a
Internal_and_external_angles
Equiangular and equilateral polygon
equilateral (all sides have the same length). Regular polygons may be either convex or star. In the limit, a sequence of regular polygons with an increasing
Regular_polygon
Quadrilateral symmetric across a diagonal
particularly if it is not convex. Every kite is an orthodiagonal quadrilateral (its diagonals are at right angles) and, when convex, a tangential quadrilateral
Kite_(geometry)
CONVEX
CONVEX
CONVEX
CONVEX
Female
Czechoslovakian
, downy-cheeked, or, soft-haired.
Girl/Female
American, Armenian, Australian, British, Chinese, Christian, Danish, Dutch, English, Finnish, French, German, Greek, Italian, Jamaican, Swedish, Swiss
A Crown of Garland; Crown; Garland; Crowned in Victory; Victorious
Boy/Male
Muslim
Victories, Conquests
Girl/Female
American, British, English
Bright Friend
Surname or Lastname
English
English : habitational name from a place so named near Woodstock in Oxfordshire.
Biblical
the physic or medicine of God
Girl/Female
Indian
Amazing
Boy/Male
Indian, Parsi
Star
Girl/Female
Teutonic
Hard working.
Boy/Male
Tamil
Courageous
CONVEX
CONVEX
CONVEX
CONVEX
CONVEX
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.
n.
The state of being convex; the exterior surface of a convex body; roundness.
n.
A saber with a much curved blade having the edge on the convex side, -- in use among Mohammedans, esp., the Arabs and persians.
n.
A convex body or surface.
n.
Convexity.
n.
A small convex hollow prominence on the surface of a shell or a coral.
a.
Concave on one side and convex on the other, as an eggshell or a crescent.
pl.
of Convexity
n.
A part, as a flange, which is hollowed out to fit upon a convex surface and serve as a means of attachment or support.
n.
The state of being convex; convexity.
adv.
In a convex form; as, a body convexly shaped.
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.
a.
Plane or flat on one side, and convex on the other; as, a plano-convex lens. See Convex, and Lens.
a.
Convex on both sides; double convex. See under Convex, a.
a.
Cut flat on the reverse, and with a convex face formed of triangular facets in rows; -- said of diamonds and other precious stones. See Rose diamond, under Rose. Cf. Brilliant, n.
a.
Convex on one side, and flat on the other; plano-convex.
v. t.
To make circular, spherical, or cylindrical; to give a round or convex figure to; as, to round a silver coin; to round the edges of anything.
n.
A drinking glass, without a foot or stem; -- so called because originally it had a pointed or convex base, and could not be set down with any liquor in it, thus compelling the drinker to finish his measure.
dv.
In a convex form; convexly.
a.
Made convex; protuberant in a spherical form.