Continuation methods do not universally solve non-convex optimization problems. In complex non-convex feature spaces, applying the continuation method can generate a computationally intractable number of objective functions, meaning that NP-hard problems remain NP-hard. Furthermore, some non-convex problems remain non-convex regardless of the extent of blurring (e.g., $J(\Theta)=-\Theta^{T}\Theta$). Additionally, blurring the space can create a false convex structure, forcing the solution path toward inferior local minima. While local minima and saddle points are problematic, sparsity is often a more significant challenge in high-dimensional feature spaces.