Convex Optimization

strongly convex

A function is strongly convex on S if there exists an $m>0$ such that
$${▽}^{2}f(x)⪰mI$$
for all $x\in S$.

integration of an increasing function is convex

Let $f$ be a real valued differentiable function defined for all $x\ge a$. Consider a function $F$ defined by $F(x)={\int }_a^{x}f(t)dt$. If $f$ is increasing on any interval, then on that interval $F$ is convex.