Convergence of Gibbs Measures Associated with Simulated Annealing

We start with an explanation of Simulated Annealing. In order to do this, we quote the paper “Convergence of Gibbs Measures Associated with Simulated Annealing” [CHK], by professors Dennis Cox of the Rice University Statistics department, Robert Hardt of the Rice University Mathematics department, and Petr Klouček of the University of Houston Texas Learning and Computation Center, which states that “Simulated annealing is a stochastic optimization algorithm that mimics the physical process of a thermodynamic system settling into a state of minimal energy while lowering the ‘temperature.’” When a system is at a high temperature, the particles in the system are more spread out, and have a high amount of energy. In contrast, when the system is near absolute zero, the particles concentrate on the system and move very slowly. Annealing explains this process. Simulated annealing is given by a Gibbs measure, which we now describe: