Convex and discrete geometry Convex sets: basic notions Concept
Convex cone
Summary
A convex cone is a subset of a real vector space that is closed under addition and under multiplication by positive scalars. It is the same as a set that is both a cone and convex. Convex cones describe the solution sets of homogeneous linear inequalities, orders on vector spaces, and the feasible regions of conic optimisation. Examples are the nonnegative orthant and the cone of positive semidefinite matrices.
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About this page
| Tag | 6VE4KA12VD |
|---|---|
| URI | m2://6VE4KA12VD |
| Kind | concept |
| Writing | W0 stub |
| MSC | 52A20, 46A55 |
| Specializes | Convex set |
| Same as |
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Used by
- Dual cone
- Minkowski–Weyl theorem
- Normal fan
- Edge-of-the-wedge theorem
- Proper cone
- Laplace transform on a convex cone
- Pointed cone
- M. Riesz extension theorem
- Farkas' lemma
- Gordan's lemma