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YouTube Videos – Convex set and Related Articles

Illustration of a convex set which looks somewhat like a deformed circle. The (black) line segment joining points x and y lies completely within the (green) set. Since this is true for any points x and y within the set that we might choose, the set is convex.

Illustration of a non-convex set. Since the red part of the (black and red) line-segment joining the points x and y lies outside of the (green) set, the set is non-convex.

A function is convex if and only if its epigraph, the region (in green) above its graph (in blue), is a convex set.

Image: Minkowski sum graph vector version