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Many high dimensional optimization problems can be reformulated into aproblem of finding theoptimal state path under an equivalent state space modelsetting. In this article, we present a general emulation strategy fordeveloping a state space model whose likelihood function (or posteriordistribution) shares the same general landscape as the objective function ofthe original optimization problem. Then the solution of the optimizationproblem is the same as the optimal state path that maximizes the likelihoodfunction or the posterior distribution under the emulated system. To find suchan optimal path, we adapt a simulated annealing approach by inserting atemperature control into the emulated dynamic system and propose a novelannealed Sequential Monte Carlo (SMC) method that effectively generating MonteCarlo sample paths utilizing samples obtained on the high temperature scale.Compared to the vanilla simulated annealing implementation, annealed SMC is aniterative algorithm for state space model optimization that directly generatesstate paths from the equilibrium distributions with a decreasing sequence oftemperatures through sequential importance sampling which does not requireburn-in or mixing iterations to ensure quasi-equilibrium condition. Severalapplications of state space model emulation and the corresponding annealed SMCresults are demonstrated.

State Space Emulation and Annealed Sequential Monte Carlo for High Dimensional Optimization