STRONGLY CONVEX FUNCTION

Strongly convex function - Arises for f in C^2: eigenvalues of hessian are bounded away from zero (from below): there exists K > 0 such that h'H_f(x)h >= K||h||^2 for all h in R^n. For example, the function exp(-x) is strictly convex on R, but its second derivative is exp(-x), which is not bounded away from zero. The minimum is not achieved because the function approaches its infimum of zero without achieving it for any (finite) x. Strong convexity rules out such asymptotes.