Efficient constrained optimization: from the deterministic past to the stochastic future

Finally, we note that a major benefit of our variational approach is that we expect to duplicate the complete theory of solutions obtained by the first author for the deterministic case. In particular, we will obtain efficient methods for closed form solution for simpler problems and/or a new, efficient theory of numerical solutions, with a maximal, pointwise, a priori error estimate of O(h3/2), for more difficult stochastic optimization problems. This includes a theory of constraint optimization with general equality and inequality constraints. An additional benefit of our approach is that major problems in the deterministic calculus of variations/optimal control theory can be compared to their associated stochastic problems since each can be efficiently solved by our methods.