  We develop a quadratic regularization approach for the solution of
high-dimensional multistage stochastic optimization problems characterized by a
potentially large number of time periods/stages (e.g. hundreds), a
high-dimensional resource state variable, and a Markov information process. The
resulting algorithms are shown to converge to an optimal policy after a finite
number of iterations under mild technical assumptions. Computational
experiments are conducted using the setting of optimizing energy storage over a
large transmission grid, which motivates both the spatial and temporal
dimensions of our problem. Our numerical results indicate that the proposed
methods exhibit significantly faster convergence than their classical
counterparts, with greater gains observed for higher-dimensional problems.
