Markov chain Monte Carlo methods for global optimization.

摘要

All topics in this dissertation are centered around global optimization problems. The major part of the dissertation is dedicated to Markov chain Monte Carlo (MCMC) methods for solving global optimization problems. Emphasis is placed on the class of simulated annealing algorithms developed by Romeijn and Smith. First, we present and analyze an implementation technique for simulated annealing, which is called the box technique. Second, based on adaptive search theory, we propose an analytically derived cooling schedule for simulated annealing. Third, we extend the domain of simulated annealing from compact bodies in high dimensional real vectors to any bounded sets in high dimensional integer lattices. The rest of the dissertation is allocated to an introduction to the transformation from infinite horizon optimization problems to global optimization problems, which is a novel way of attacking general dynamical decision making problems.