Statistical Methods for Hybrid Optimization

University Of California-Santa Cruz, Santa Cruz CA

Investigators

Abstract

This project combines local numerical optimization routines from applied mathematics with flexible global models from statistics to create efficient hybrid optimization routines. These routines can address difficult optimization problems involving multi-dimensional and multi-modal functions. We focus on pattern search as our local routine and treed Gaussian processes as our statistical emulator. We develop an implementation in an asynchronous parallel computing environment, and allow for both known and hidden constraints. We also explore optimization of stochastic functions and optimization under uncertainty, as well as robust optimization. This project solves difficult optimization problems by combining tools from the fields of applied mathematics and statistics. By intertwining efficient local numerical routines with global statistical emulators, we develop efficient and robust algorithms for maximizing or minimizing functions. This inherently inter-disciplinary work has immediate applications in a wide range of fields, and we demonstrate its effectiveness on problems from electrical engineering and hydrology.