#### Interpolated points are contained in the set

In general, a set or function is convex if, for any two points within it, the line segment connecting them lies entirely within the set or below/on the function's graph. In the perspective of function, function is convex if the line segment between any two points on its graph lies below or on the graph

- When any two points are selected, all points on the line segment connecting these two points also belong to the function or set.

- When any two points are selected, if all points between these two points belong to the function or set, we say that this function or set is
**strictly convex**.

Second Derivative positive is equivalent to convexity. In a same sense, the multivariate is convex iff

**Hessian Matrix**’s all Eigenvalue is larger than 0.#### Strictly Convex

There should not be flat regions. Iff

**Hessian Matrix**’s all Eigenvalue > 0, there are no flat regions and strictly convex.#### Properties

- The sum of any two convex functions is convex

- The maximum of any two convex functions is convex