Continuation methods aim to minimize a complex cost function $J(\Theta)$ by constructing a sequence of increasingly difficult cost functions $\left\{J^{(0)}, \dots, J^{(n)}\right\}$, where $J^{(0)}$ is the most smoothed (easiest to optimize) and $J^{(n)}=J(\Theta)$ is the original function. Smoothing is often achieved by "blurring" the cost function via sampling, such as approximating it with J^{(i)}(Theta)=mathop{mathbb{E}}_{Theta'simmathcal{N}(Theta';Theta,sigma^{(i)2})}J(Theta'). Optimization begins at $J^{(0)}$, where the blurred non-convex space resembles a convex one, providing an effective initial starting point for the subsequent function $J^{(1)}$. Iterating this process through $J^{(n)}$ typically yields a superior local minimum for the original optimization problem, though it does not guarantee finding the global minimum.