A locally adapted reduced basis method for solving risk-averse pde-constrained optimization problems

Conference Paper

The numerical solution of risk-averse PDE-constrained optimization problems requires substantial computational effort resulting from the discretization of the underlying PDE in both the physical and stochastic dimensions. To practically solve problems with high-dimensional uncertainties, one must intelligently manage the individual discretization fidelities throughout the optimization iteration. In this work, we combine an inexact trust-region algorithm with the recently developed local reduced basis approximation to efficiently solve risk-averse optimization problems with PDE constraints. The main contribution of this work is a numerical framework for systematically constructing surrogate models for the trust-region subproblem and the objective function using local reduced basis approximations. We demonstrate the effectiveness of our approach through a numerical example.

Full Text

Duke Authors

Cited Authors

  • Zou, Z; Kouri, D; Aquino, W

Published Date

  • January 1, 2018

Published In

  • Aiaa Non Deterministic Approaches Conference, 2018

Volume / Issue

  • 0 / 209969

International Standard Book Number 13 (ISBN-13)

  • 9781624105296

Digital Object Identifier (DOI)

  • 10.2514/6.2018-2174

Citation Source

  • Scopus