A Globally Convergent Method to Accelerate PDE-constrained Optimization Using On-the-fly Model Hyperreduction

Abstract

We present a numerical method to efficiently solve side-constrained optimization problems governed by large-scale nonlinear systems of equations using an augmented Lagrangian framework. A globally convergent, hyperreduced trust-region framework is embedded in the proposed framework to accelerate the optimization process in each major iteration. The trust-region framework constructs a hyperreduction model via empirical quadrature procedure (EQP) on-the-fly, which completely avoids an offline training phase. A numerical experiment is performed on a shape optimization problem to verify and demonstrate the efficiency of the proposed work. Speedup of around 3x (for all computational costs, even cost traditionally considered “offline” such as snapshot collection and data compression) relative to a standard optimization approach that does not leverage model reduction is shown.