Based on the theoretical framework recently proposed by Bonifacius and Neitzel (Math Control Relat Fields 8(1):1–34, 2018. https://doi.org/10.3934/mcrf.2018001) we discuss the sequential quadratic programming (SQP) method for the numerical solution of an optimal control problem governed by a quasilinear parabolic partial differential equation. Following well-known techniques, convergence of the method in appropriate function spaces is proven under some common technical restrictions. Particular attention is payed to how the second order sufficient conditions for the optimal control problem and the resulting \(L^2\)-local quadratic growth condition influence the notion of “locality” in the SQP method. Further, a new regularity result for the adjoint state, which is required during the convergence analysis, is proven. Numerical examples illustrate the theoretical results.

基于Bonifacius和Neitzel最近提出的理论框架（数学控制相关字段8（1）：1–34，2018. https://doi.org/10.3934/mcrf.2018001），我们讨论了顺序二次编程（SQP）拟线性抛物型偏微分方程的最优控制问题数值解的一种方法。遵循众所周知的技术，在某些常见技术限制下证明了该方法在适当的功能空间中的收敛性。特别要注意的是如何针对最佳控制问题的二阶充分条件以及所得到的\（L ^ 2 \）-局部二次生长条件影响SQP方法中的“局部性”概念。此外，证明了收敛分析过程中需要的伴随状态的新规律性结果。数值例子说明了理论结果。