  We propose new sequential simulation-optimization algorithms for general
convex optimization via simulation problems with high-dimensional discrete
decision space. The performance of each choice of discrete decision variables
is evaluated via stochastic simulation replications. If an upper bound on the
overall level of uncertainties is known, our proposed simulation-optimization
algorithms utilize the discrete convex structure and are guaranteed with high
probability to find a solution that is close to the best within any given
user-specified precision level. The proposed algorithms work for any general
convex problem and the efficiency is demonstrated by proven upper bounds on
simulation costs. The upper bounds demonstrate a polynomial dependence on the
dimension and scale of the decision space. For some discrete optimization via
simulation problems, a gradient estimator may be available at low costs along
with a single simulation replication. By integrating gradient estimators, which
are possibly biased, we propose simulation-optimization algorithms to achieve
optimality guarantees with a reduced dependence on the dimension under moderate
assumptions on the bias.
