10.6084/m9.figshare.1332462
Robert B. Gramacy
Genetha A. Gray
Sébastien Le Digabel
Herbert K. H. Lee
Pritam Ranjan
Garth Wells
Stefan M. Wild
Modeling an Augmented Lagrangian for Blackbox Constrained Optimization
2015
Taylor & Francis Group
Augmented Lagrangian
sensitivity analysis
Blackbox Constrained Optimization Constrained blackbox optimization
response surface modeling
modeling effort
improvement heuristics
objective function
optimization framework
Gaussian process surrogates
nontrivial constraints
approach
programming literature
Supplementary materials
problem
2015-07-09 08:02:13
article
https://tandf.figshare.com/articles/Modeling_an_Augmented_Lagrangian_for_Blackbox_Constrained_Optimization/1332462
<p>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. Supplementary materials for this article are available online.</p>