Analysis of the SQP Method for Hyperbolic PDE-Constrained Optimization in Acoustic Full Waveform Inversion
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866909807238184960 |
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| author | Ammann, Luis Yousept, Irwin |
| author_facet | Ammann, Luis Yousept, Irwin |
| contents | In this paper, the SQP method applied to a hyperbolic PDE-constrained optimization problem is considered. The model arises from the acoustic full waveform inversion in the time domain. The analysis is mainly challenging due to the involved hyperbolicity and second-order bilinear structure. This notorious character leads to an undesired effect of loss of regularity in the SQP method, calling for a substantial extension of developed parabolic techniques. We propose and analyze a novel strategy for the well-posedness and convergence analysis based on the use of a smooth-in-time initial condition, a tailored self-mapping operator, and a two-step estimation process along with Stampacchia's method for second-order wave equations. Our final theoretical result is the R-superlinear convergence of the SQP method. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_05158 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Analysis of the SQP Method for Hyperbolic PDE-Constrained Optimization in Acoustic Full Waveform Inversion Ammann, Luis Yousept, Irwin Numerical Analysis Optimization and Control In this paper, the SQP method applied to a hyperbolic PDE-constrained optimization problem is considered. The model arises from the acoustic full waveform inversion in the time domain. The analysis is mainly challenging due to the involved hyperbolicity and second-order bilinear structure. This notorious character leads to an undesired effect of loss of regularity in the SQP method, calling for a substantial extension of developed parabolic techniques. We propose and analyze a novel strategy for the well-posedness and convergence analysis based on the use of a smooth-in-time initial condition, a tailored self-mapping operator, and a two-step estimation process along with Stampacchia's method for second-order wave equations. Our final theoretical result is the R-superlinear convergence of the SQP method. |
| title | Analysis of the SQP Method for Hyperbolic PDE-Constrained Optimization in Acoustic Full Waveform Inversion |
| topic | Numerical Analysis Optimization and Control |
| url | https://arxiv.org/abs/2405.05158 |