Relative interior
From Wikipedia, the free encyclopedia
In mathematics, the relative interior of a set is a refinement of the concept of the interior, which is often more useful when dealing with low-dimensional sets placed in higher-dimensional spaces. Intuitively, the relative interior of a set contains all points which are not on the "edge" of the set, relative to the smallest subspace in which this set lies.
Formally, the relative interior of a set S (denoted relint(S)) is defined as its interior within the affine hull of S. In other words,
where aff(S) is the affine hull of S, and Nε(x) is a ball of radius ε centered on x. Any metric can be used for the construction of the ball; all metrics define the same set as the relative interior.
[edit] References
- Boyd, Stephen; Lieven Vandenberghe (2004). Convex Optimization. Cambridge: Cambridge University Press, p. 23. ISBN 0 521 83378 7.
