Linked from

The 15 pages that link to Extreme point, each with the reason it gives.

• Linear programmingRelated: When an optimum exists, some extreme point achieves it.

• Convex hullRelated: For finite point sets, extreme points of the hull are precisely its vertices.

• PolyhedronRelated: Extreme points are the vertices singled out by a polyhedron's geometry.

• Vertex (geometry)Related: For convex polygons, the vertices are precisely the extreme points.

• Convex geometryRelated: Extreme points capture the indivisible corners of convex sets.

• Feasible regionRelated: Linear objectives over polyhedra attain finite optima at extreme points when an optimum exists.

• Carathéodory's theoremRelated: Extreme-point ideas connect finite convex representations to the structure of convex sets.

• Convex combinationRelated: Extreme points cannot be written as nontrivial convex combinations of other points in the set.

• Simplex algorithmRelated: Linear programs with finite optima have an optimal extreme point.

• Convex bodyRelated: Extreme points identify the body’s non-decomposable boundary locations.

• Linear programming relaxationRelated: Linear objectives attain optima at extreme points of bounded polyhedral regions.

• Krein–Milman theoremBroader topic: These are the points whose closed convex hull recovers the entire set.

• Banach–Stone theoremRelated: Extreme points of dual unit balls help identify evaluation functionals at points of the compact spaces.

• Ryll-Nardzewski fixed-point theoremRelated: Extreme points link the convex geometry of the set to fixed-point arguments.

• Shapley–Folkman lemmaRelated: The representation argument reduces most summands to points of their original sets.