Extended Pincus theorems and convergence of simulated annealing

Abstract

Pincus’ 1968 formula for the (unique) global minimum of a continuous function on a compact set in E n is extended to finite multiple optima and to discrete and special variants. The impact of these on associated ergodic irreducible aperiodic Markov chain computation (Pincus 1970)—currently called ‘simulated annealing’—is exemplified and assessed leading to grave concern about what current simulated annealing processes may converge to, instead of optima.