  We consider the Scenario Convex Program (SCP) for two classes of optimization
problems that are not tractable in general: Robust Convex Programs (RCPs) and
Chance-Constrained Programs (CCPs). We establish a probabilistic bridge from
the optimal value of SCP to the optimal values of RCP and CCP in which the
uncertainty takes values in a general, possibly infinite dimensional, metric
space. We then extend our results to a certain class of non-convex problems
that includes, for example, binary decision variables. In the process, we also
settle a measurability issue for a general class of scenario programs, which to
date has been addressed by an assumption. Finally, we demonstrate the
applicability of our results on a benchmark problem and a problem in fault
detection and isolation.
