  Constrained blackbox optimization is a difficult problem, with most
approaches coming from the mathematical programming literature. The statistical
literature is sparse, especially in addressing problems with nontrivial
constraints. This situation is unfortunate because statistical methods have
many attractive properties: global scope, handling noisy objectives,
sensitivity analysis, and so forth. To narrow that gap, we propose a
combination of response surface modeling, expected improvement, and the
augmented Lagrangian numerical optimization framework. This hybrid approach
allows the statistical model to think globally and the augmented Lagrangian to
act locally. We focus on problems where the constraints are the primary
bottleneck, requiring expensive simulation to evaluate and substantial modeling
effort to map out. In that context, our hybridization presents a simple yet
effective solution that allows existing objective-oriented statistical
approaches, like those based on Gaussian process surrogates and expected
improvement heuristics, to be applied to the constrained setting with minor
modification. This work is motivated by a challenging, real-data benchmark
problem from hydrology where, even with a simple linear objective function,
learning a nontrivial valid region complicates the search for a global minimum.
