Analysis of the SQP Method for Hyperbolic PDE-Constrained Optimization in Acoustic Full Waveform Inversion
<|reference_start|>Analysis of the SQP Method for Hyperbolic PDE-Constrained Optimization in Acoustic Full Waveform Inversion: 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.<|reference_end|>
@article{ammann2024analysis,
    title={Analysis of the SQP Method for Hyperbolic PDE-Constrained Optimization
  in Acoustic Full Waveform Inversion},
    author={Luis Ammann and Irwin Yousept},
    journal={arXiv preprint arXiv:2405.05158},
    year={2024},
    archivePrefix={arXiv},
    eprint={2405.05158},
    primaryClass={math.NA cs.NA math.OC}
}