If f is a quadratic form in one variable, it can be written as f (x) = ax2. In this case, f is convex if a ≥ 0 and concave if a ≤ 0.

Is a quadratic convex?

The quadratic objective function may be convex -- which makes the problem easy to solve -- or non-convex, which makes it very difficult to solve. The "best" QPs have Hessians that are positive definite (in a minimization problem) or negative definite (in a maximization problem).

Is a quadratic convex or concave?

2 Answers. For a quadratic function f(x)=ax2+bx+c , if a>0 , then f is concave upward everywhere, if a<0 , then f is concave downward everywhere.