constituents requirements Iterative methods require a starting point x^{(0)} such that: x^{(0)} \in \text{dom } f sublevel set S = \left\{x \mid f\left(x\right) \leq f\left(x^{(0)}\right)\right\} is closed additional information strong convexity f is strongly convex on S if there exists m > 0 such that:
\begin{align} \nabla^{2}f\left(x\right) \succeq mI, \forall x \in S \end{align}
if f is strongly convex for x, y \in S, we have:
\begin{align} f\left(y\right) \geq f\left(x\right) + \nabla f\left(x\right)^{T} \left(y-x\right) + \frac{m}{2} \norm{x-y}_{2}^{2} \end{align}
and thus we can get a nice convergence criteria:
\begin{align} f\left(x\right) - p^{*} \leq \frac{1}{2m}\norm{\nabla f\left(x\right)}_{2}^{2} \end{align}
various iterative methods descent method