  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.
