is convex if, given any two points in the subset, the subset contains the whole line segment that joins them. Equivalently, a convex set or a convex region...

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...

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...

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...

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...

problems in mathematical programming can be formulated as problems on convex sets or convex bodies. Six kinds of problems are particularly important:: Sec.2 ...

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

whose topology is generated by translations of balanced, absorbent, convex sets. Alternatively they can be defined as a vector space with a family of...

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...

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...

 Theorem 2.3.23  The concepts of convex sets and convex components are used in a proof that every totally ordered set endowed with the order topology is...

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...

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 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...

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

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....

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,...

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...

example, every convex combination of two points lies on the line segment between the points. A set is convex if it contains all convex combinations of...

{O}}(G)} stand for the set of holomorphic functions on G. For a compact set K ⊂ G {\displaystyle K\subset G} , the holomorphically convex hull of K is K ^ G...

Examples of convex curves include the convex polygons, the boundaries of convex sets, and the graphs of convex functions. Important subclasses of convex curves...

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...

corners or vertices. A convex polyhedron is a polyhedron that bounds a convex set. Every convex polyhedron can be constructed as the convex hull of its vertices...

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...

In mathematics, convex geometry is the branch of geometry studying convex sets, mainly in Euclidean space. Convex sets occur naturally in many areas: computational...

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...

used to solve non-differentiable convex optimization problems. Many interesting problems can be formulated as convex optimization problems of the form...

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. For...

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...