Abstract: Many high-dimensional optimization problems can be reformulated as finding the optimal path under an equivalent state-space model setting. Here, we present a general emulation strategy for developing a state-space model with a likelihood function (or posterior distribution) that shares the same general landscape as that of the original objective function. Then, the solution of the optimization problem is the same as the optimal state path that maximizes the likelihood function. To find such an optimal path, we adapt a simulated annealing approach by inserting a temperature control into the emulated dynamic system, and propose a novel annealed sequential Monte Carlo (SMC) method that effectively generates Monte Carlo sample paths based on samples obtained previously on a higher temperature scale. Compared with the vanilla simulated annealing implementation, the annealed SMC is an iterative algorithm for state-space model optimization that generates state paths directly from the equilibrium distributions using a decreasing sequence of temperatures and sequential importance sampling, which does not require burn-in or mixing iterations to ensure a quasi-equilibrium condition. Lastly, we demonstrate the proposed method by presenting several emulation examples and the corresponding simulation results.

Key words and phrases: Emulation, optimization, sequential Monte Carlo, simulated annealing, state space model.