This talk will focus on the application of Markov Chain Monte Carlo methods to stochastic optimization models of the form:

$$\min_{x^{T+1}\in X} E[\sum_{t=1}^T f_t(x_t,x_{t+1})],$$

where $x^t=(x_1,\ldots,x_t)$, $X$ includes nonanticipativity constraints, and $f_t$ is convex with extended value to include

additional constraints. The talk will describe conditions for asymptotic convergence of the Markov chain of a version of

particle filtering that maintains a fixed number $N$ particles in each period. Extensions of the results will be described

for robust objectives of the form:

$$\min_{x^{T+1}\in X}[\max_{\xi_1\in\Xi_1}f_1(x_1,x_2(\xi_1),\xi_1) +\max_{\xi_2(x_2(\xi_1),\xi_1)\in\Xi_2} f_2(x_2(\xi_1),x_3(\xi^2),\xi^2)+\cdots +\max_{\xi_T(x^{T}(\xi^{T-1}),\xi^{T-1})\in\Xi_T} f_{T}(x_{T}(\xi^{T-1}),x_{T+1}(\xi^T),\xi^T)],$$

where $\xi^t=(\xi_1,\ldots,\xi_t)$ represents random observations up to period $t$ and $\Xi_t$ is a compact uncertainty set for

each period's realizations. We will particularly consider cases with linear dynamics and methods for identifying affine policies

from the states of the Markov chain.