Optimization Under Constraints by Applying an Asymmetric Entropy Measure

Complex functions, such as the output of computer simulators, can be difficult to optimize. The task becomes even more difficult when only some of the function evaluations return real numbers and others simply fail to return a value. We combine statistical emulation, classification, sequential design, and optimization with an asymmetric entropy measure to solve the thorny problem of finding an optimum along a constraint boundary. This approach is demonstrated on simulated examples and a real problem in groundwater remediation.