This paper considers the regularization continuation method and the trust-region updating strategy for the nonlinearly equality-constrained optimization problem. Namely, it uses the inverse of the regularization quasi-Newton matrix as the pre-conditioner to improve its computational efficiency in the well-posed phase, and it adopts the inverse of the regularization two-sided projection of the Hessian as the pre-conditioner to improve its robustness in the ill-conditioned phase. Since it only solves a linear system of equations at every iteration and the sequential quadratic programming (SQP) needs to solve a quadratic programming subproblem at every iteration, it is faster than SQP. Numerical results also show that it is more robust and faster than SQP (the built-in subroutine fmincon.m of the MATLAB2020a environment and the subroutine SNOPT executed in GAMS v28.2 (2019) environment). The computational time of the new method is about one third of that of fmincon.m for the large-scale problem. Finally, the global convergence analysis of the new method is also given.

翻译：本文研究了非线性等式约束优化问题的正则化连续方法及信赖域更新策略。具体而言，在适定阶段采用正则化拟牛顿矩阵的逆作为预条件子以提高计算效率，在病态阶段则采用正则化Hessian矩阵双侧投影的逆作为预条件子以增强鲁棒性。由于该方法每步迭代仅需求解线性方程组，而序列二次规划(SQP)每步需求解二次规划子问题，因此其求解速度优于SQP。数值结果表明，该方法在鲁棒性和计算速度上均优于SQP（MATLAB2020a环境内置子程序fmincon.m及GAMS v28.2 (2019)环境下的SNOPT子程序）。对于大规模问题，新方法的计算时间约为fmincon.m的三分之一。最后，本文还给出了新方法的全局收敛性分析。