SIAM Journal on Scientific Computing, Volume 42, Issue 3, Page A1836-A1859, January 2020.
We build upon R. Estrin et al., [SIAM J. Sci. Comput., 42 (2020), pp. A1809--A1835] to develop a general constrained nonlinear optimization algorithm based on a smooth penalty function proposed by R. Fletcher [Integer and Nonlinear Programming, J. Abadie, ed., North-Holland, Amsterdam, (1970), pp. 157--175; Math. Program., 5 (1973), pp. 129--150]. Although Fletcher's approach has historically been considered impractical, we show that the computational kernels required are no more expensive than those in other widely accepted methods for nonlinear optimization. The main kernel for evaluating the penalty function and its derivatives solves structured linear systems. When the matrices are available explicitly, we store a single factorization each iteration. Otherwise, we obtain a factorization-free optimization algorithm by solving each linear system iteratively. The penalty function shows promise in cases where the linear systems can be solved efficiently, e.g., PDE-constrained optimization problems when efficient preconditioners exist. We demonstrate the merits of the approach, and give numerical results on several PDE-constrained and standard test problems.

中文翻译：

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为一般约束非线性优化实现光滑精确罚函数

SIAM科学计算杂志，第42卷，第3期，第A1836-A1859页，2020年1月。
我们以R. Estrin等人[SIAM J. Sci。Comput。，42（2020），pp。A1809--A1835]开发一种基于平滑罚函数的通用约束非线性优化算法，该算法由R. Fletcher提出[整数和非线性规划，J。Abadie编辑，北荷兰阿姆斯特丹（1970），157--175页; 数学。计划，5（1973），第129--150页]。尽管历史上一直认为Fletcher的方法不切实际，但我们证明所需的计算内核并不比其他广泛接受的非线性优化方法昂贵。评估罚函数及其导数的主要内核解决了结构化线性系统。当矩阵明确可用时，我们在每次迭代中存储一个分解因子。除此以外，通过迭代求解每个线性系统，我们获得了无因数分解的优化算法。惩罚函数在线性系统可以有效求解的情况下显示出希望，例如，当存在有效的预处理器时，PDE约束的优化问题。我们演示了该方法的优点，并给出了一些受PDE约束和标准测试问题的数值结果。