Global optimization, the Gaussian ensemble, and universal ensemble equivalence

Shortened abstract: Given a constrained minimization problem, under what conditions does there exist a related, unconstrained problem having the same minimum points? This basic question in global optimization motivates this paper, which answers it from the viewpoint of statistical mechanics. In this context, it reduces to the fundamental question of the equivalence and nonequivalence of ensembles, which is analyzed using the theory of large deviations and the theory of convex functions.