restrictedcone
Restrictedcone is a term used in convex analysis to describe a convex cone formed by restricting a base cone with linear constraints. Given a cone C in a real vector space V and a linear subspace L ⊆ V, the restrictedcone is defined as K = C ∩ L. Equivalently, if L is described by Ax = 0, then K = { x ∈ C : Ax = 0 }. The construction preserves conicity and convexity when the restriction subspace passes through the origin. If C is closed or polyhedral, the restrictedcone is likewise closed or polyhedral.
Properties of a restrictedcone follow from those of C and L. It is convex by construction, and
Examples help illustrate the concept. In R^3, let C be the nonnegative orthant { (x, y, z) :
Applications of restrictedcone include modeling feasible regions in conic optimization with linear constraints, decomposition of problems