An augmented Lagrangian trust-region method with inexact gradient evaluations to accelerate constrained optimization problems using model hyperreduction
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| Format: | Preprint |
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2024
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| _version_ | 1866909209483804672 |
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| author | Wen, Tianshu Zahr, Matthew J. |
| author_facet | Wen, Tianshu Zahr, Matthew J. |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_14827 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An augmented Lagrangian trust-region method with inexact gradient evaluations to accelerate constrained optimization problems using model hyperreduction Wen, Tianshu Zahr, Matthew J. Optimization and Control Numerical Analysis 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. |
| title | An augmented Lagrangian trust-region method with inexact gradient evaluations to accelerate constrained optimization problems using model hyperreduction |
| topic | Optimization and Control Numerical Analysis |
| url | https://arxiv.org/abs/2405.14827 |