SIAM Journal on Optimization, Volume 30, Issue 3, Page 1822-1849, January 2020.
This paper focuses on the design of sequential quadratic optimization (commonly known as SQP) methods for solving large-scale nonlinear optimization problems. The most computationally demanding aspect of such an approach is the computation of the search direction during each iteration, for which we consider the use of matrix-free methods. In particular, we develop a method that requires an inexact solve of a single QP subproblem to establish the convergence of the overall SQP method. It is known that SQP methods can be plagued by poor behavior of the global convergence mechanism. To confront this issue, we propose the use of an exact penalty function with a dynamic penalty parameter updating strategy to be employed within the subproblem solver in such a way that the resulting search direction predicts progress toward both feasibility and optimality. We present our parameter updating strategy and prove that, under reasonable assumptions, the strategy does not modify the penalty parameter unnecessarily. We close the paper with a discussion of the results of numerical experiments that illustrate the benefits of our proposed techniques.

中文翻译：

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QP解算器中具有惩罚参数更新的不精确序列二次优化

SIAM优化杂志，第30卷，第3期，第1822-1849页，2020年1月。
本文着重于解决大型非线性优化问题的顺序二次优化（通常称为SQP）方法的设计。这种方法在计算上最苛刻的方面是每次迭代期间搜索方向的计算，为此，我们考虑使用无矩阵方法。特别是，我们开发了一种方法，该方法需要单个QP子问题的不精确求解才能建立整个SQP方法的收敛性。众所周知，SQP方法可能会受到全局收敛机制行为不佳的困扰。面对这个问题 我们建议在子问题求解器中使用带有动态惩罚参数更新策略的精确惩罚函数，以使结果搜索方向预测朝着可行性和最优性发展的方式。我们提出了参数更新策略，并证明了在合理的假设下，该策略不会不必要地修改惩罚参数。在本文的最后，我们讨论了数值实验的结果，这些结果说明了我们提出的技术的优势。