Analysis of the SQP Method for Hyperbolic PDE-Constrained Optimization in Acoustic Full Waveform Inversion

TL;DR

This paper analyzes the SQP method applied to hyperbolic PDE-constrained optimization in acoustic full waveform inversion, addressing challenges from hyperbolicity and bilinear structures, and proves its R-superlinear convergence.

Contribution

It introduces a novel strategy for analyzing SQP in hyperbolic PDEs, ensuring well-posedness and convergence despite regularity loss.

Findings

Proposes a new approach for hyperbolic PDE-constrained optimization.

Establishes R-superlinear convergence of the SQP method.

Addresses regularity issues in hyperbolic PDEs with a tailored analysis.

Abstract

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.