  This article considers nonconvex global optimization problems subject to
uncertainties described by continuous random variables. Such problems arise in
chemical process design, renewable energy systems, stochastic model predictive
control, etc. Here, we restrict our attention to problems with expected-value
objectives and no recourse decisions. In principle, such problems can be solved
globally using spatial branch-and-bound (B&B). However, B&B requires the
ability to bound the optimal objective value on subintervals of the search
space, and existing techniques are not generally applicable because
expected-value objectives often cannot be written in closed-form. To address
this, this article presents a new method for computing convex and concave
relaxations of nonconvex expected-value functions, which can be used to obtain
rigorous bounds for use in B&B. Furthermore, these relaxations obey a
second-order pointwise convergence property, which is sufficient for finite
termination of B&B under standard assumptions. Empirical results are shown for
three simple examples.
