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.

翻译：本文研究了应用于双曲PDE约束优化问题的SQP方法。该模型源于时域声波全波形反演。分析的主要挑战在于所涉及的双曲性和二阶双线性结构。这一显著特征导致SQP方法中正则性丧失的不良效应，需要将现有的抛物型方法进行实质性扩展。我们提出并分析了一种新的适定性与收敛性分析策略，该策略基于光滑时间初值条件、定制化自映射算子、两步估计过程以及二阶波动方程的Stampacchia方法。最终的理论结果是SQP方法的R-超线性收敛性。