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What (who) is K-convex function - definition
K-convex 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 of the (s,S) policy in inventory control theory. The policy is characterized by two numbers and , S \geq s, such that when the inventory level falls below level , an order is issued for a quantity that brings the inventory up to level , and nothing is ordered otherwise.
convex hull
![A [[bagplot]]. The outer shaded region is the convex hull, and the inner shaded region is the 50% Tukey depth contour.](https://commons.wikimedia.org/wiki/Special:FilePath/Bagplot.png?width=200 "A [[bagplot]]. The outer shaded region is the convex hull, and the inner shaded region is the 50% Tukey depth contour.")
![An [[oloid]], the convex hull of two circles in 3d space](https://commons.wikimedia.org/wiki/Special:FilePath/Oloid structure.svg?width=200 "An [[oloid]], the convex hull of two circles in 3d space")
![Partition of seven points into three subsets with intersecting convex hulls, guaranteed to exist for any seven points in the plane by [[Tverberg's theorem]]](https://commons.wikimedia.org/wiki/Special:FilePath/Tverberg heptagon.svg?width=200 "Partition of seven points into three subsets with intersecting convex hulls, guaranteed to exist for any seven points in the plane by [[Tverberg's theorem]]")
![The [[witch of Agnesi]]. The points on or above the red curve provide an example of a closed set whose convex hull is open (the open [[upper half-plane]]).](https://commons.wikimedia.org/wiki/Special:FilePath/Versiera007.svg?width=200 "The [[witch of Agnesi]]. The points on or above the red curve provide an example of a closed set whose convex hull is open (the open [[upper half-plane]]).")
NOTION IN TOPOLOGICAL VECTOR SPACES
Convex envelope; Closed convex hull; Convex Hull; Convex span; Convex closure; Minimum convex polygon; Applications of convex hulls
<mathematics, graphics> For a set S in space, the smallest
convex set containing S. In the plane, the convex hull can
be visualized as the shape assumed by a rubber band that has
been stretched around the set S and released to conform as
closely as possible to S.
(1997-08-03)
Convex hull
NOTION IN TOPOLOGICAL VECTOR SPACES
Convex envelope; Closed convex hull; Convex Hull; Convex span; Convex closure; Minimum convex polygon; Applications of convex hulls
In geometry, the convex hull or convex envelope or convex closure of a shape is the smallest convex set that contains it. The convex hull may be defined either as the intersection of all convex sets containing a given subset of a Euclidean space, or equivalently as the set of all convex combinations of points in the subset.
