a set of points is convex if it contains every line segment between two points in the set. Equivalently, a convex set or a convex region is a set that...

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...

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...

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...

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...

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...

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...

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

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

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

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...

logarithmically-convex. A Reinhardt domain D is called logarithmically convex if the image λ ( D ∗ ) {\displaystyle \lambda (D^{*})} of the set D ∗ = { z =...

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...

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

reflecting. The convex polyhedron is well-defined with several equivalent standard definitions, one of which is a polyhedron that is a convex set, or the polyhedral...

function p : X → R {\displaystyle p:X\to \mathbb {R} } which is subadditive, convex, and satisfies p ( 0 ) ≤ 0 {\displaystyle p(0)\leq 0} is also positively...

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....

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...

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

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...

double lattice packing density of any convex set, and more generally for the optimal packing density of any convex set. The United Kingdom, since 1982, has...

set – Convex and balanced set Balanced set – Construct in functional analysis Bornivorous set – A set that can absorb any bounded subset Bounded set (topological...

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,...

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...

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 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...