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...

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...

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...

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

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...

 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...