Convex

Resources

Boyd, Stephen, and Lieven Vandenberghe. 2004. “Convex Optimization.” http://www.cambridge.org.

Main Idea

In a Vector Space, a subset is convex if it contains any possible line segment joining two of the points.

Details

Let $V$ be a vector space, and $U \subset V$ is some subset. Then $U$ is convex if

(1 + t) f + t g \in U, \forall t \in [0, 1], \forall f, g \in U .

Note that this definition does not even require a Normed Vector Space!