An augmented Lagrangian trust-region method with inexact gradient evaluations to accelerate constrained optimization problems using model hyperreduction
<|reference_start|>An augmented Lagrangian trust-region method with inexact gradient evaluations to accelerate constrained optimization problems using model hyperreduction: We present an augmented Lagrangian trust-region method to efficiently solve constrained optimization problems governed by large-scale nonlinear systems with application to partial differential equation-constrained optimization. At each major augmented Lagrangian iteration, the expensive optimization subproblem involving the full nonlinear system is replaced by an empirical quadrature-based hyperreduced model constructed on-the-fly. To ensure convergence of these inexact augmented Lagrangian subproblems, we develop a bound-constrained trust-region method that allows for inexact gradient evaluations, and specialize it to our specific setting that leverages hyperreduced models. This approach circumvents a traditional training phase because the models are built on-the-fly in accordance with the requirements of the trust-region convergence theory. Two numerical experiments (constrained aerodynamic shape design) demonstrate the convergence and efficiency of the proposed work. A speedup of 12.7x (for all computational costs, even costs traditionally considered "offline" such as snapshot collection and data compression) relative to a standard optimization approach that does not leverage model reduction is shown.<|reference_end|>
@article{wen2024an,
    title={An augmented Lagrangian trust-region method with inexact gradient
  evaluations to accelerate constrained optimization problems using model
  hyperreduction},
    author={Tianshu Wen and Matthew J. Zahr},
    journal={arXiv preprint arXiv:2405.14827},
    year={2024},
    archivePrefix={arXiv},
    eprint={2405.14827},
    primaryClass={math.OC cs.NA math.NA}
}