Linked from

The 45 pages that link to Convex set, each with the reason it gives.

• Linear programmingNarrower topic: Intersections of linear half-spaces form convex feasible regions.

• Jensen's inequalityNarrower topic: Convex functions and their epigraphs are defined through this geometric property.

• Convex hullNarrower topic: The hull is the smallest set with this defining property that contains the given points.

• Interval (mathematics)Narrower topic: Intervals are exactly the convex subsets of the real line.

• PolyhedronNarrower topic: Intersections of half-spaces are convex, so every polyhedron has this property.

• Extreme pointNarrower topic: Extreme points are defined relative to a convex set and its line segments.

• Carathéodory's theoremNarrower topic: Convex hulls and convex combinations are defined through this closure property.

• Convex combinationNarrower topic: Convex sets contain every convex combination of their points.

• Convex polygonNarrower topic: The polygon’s defining property is convexity applied to its interior.

• Simplex algorithmNarrower topic: Convexity explains why local improvement across edges can find a global optimum.

• Convex bodyNarrower topic: Convexity is the defining condition inherited by every convex body.

• Support functionNarrower topic: For closed convex sets, the support function captures the set completely.

• Minkowski's theorem (geometry of numbers)Narrower topic: Convexity is one of the geometric conditions that makes the lattice-point guarantee hold.

• Gérard DebreuNarrower topic: Convexity assumptions help make equilibrium existence proofs work.

• Helly's theoremNarrower topic: Convexity is the geometric condition that makes the intersection criterion work.

• Gauss–Lucas theoremNarrower topic: The convex-hull conclusion relies on this geometric notion of containment.

• Reuleaux triangleNarrower topic: The Reuleaux triangle is convex, a broader property that does not imply constant width.

• Ellipsoid methodNarrower topic: The method's cuts preserve a convex feasible region inside each enclosing ellipsoid.

• Tverberg's theoremNarrower topic: The theorem concerns intersections of convex sets formed from point groups.

• Cone (convex analysis)Narrower topic: A convex cone adds nonnegative scaling to this defining closure property.

• Hyperplane separation theoremNarrower topic: Convexity is the structural assumption that makes a separating hyperplane possible.

• Erdős–Nagy theoremNarrower topic: Convexity is the defining property of the theorem’s final polygon.

• Shapley–Folkman lemmaNarrower topic: The lemma quantifies how sums of arbitrary sets approach the behavior of convex sets.