Abstract An efficient preconditioning technique used earlier for two-by-two block matrix systems with square matrix blocks is shown to be applicable also for a state variable box-constrained optimal control problem. The problem is penalized by a standard regularization term for the control variable and for the box-constraint, using a Moreau–Yosida penalization method. It is shown that there occur very few nonlinear iteration steps and also few iterations to solve the arising linearized equations on the fine mesh. This holds for a wide range of the penalization and discretization parameters. The arising nonlinearity can be handled with a hybrid nonlinear-linear procedure that raises the computational efficiency of the overall solution method.

中文翻译：

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一种状态盒约束最优控制问题的有效预处理方法

摘要 先前用于具有方阵块的 2×2 块矩阵系统的有效预处理技术也适用于状态变量框约束最优控制问题。使用 Moreau-Yosida 惩罚方法，该问题受到控制变量和框约束的标准正则化项的惩罚。结果表明，在精细网格上求解线性化方程的非线性迭代步骤很少，迭代次数也很少。这适用于广泛的惩罚和离散化参数。产生的非线性可以用混合非线性-线性程序处理，从而提高整体求解方法的计算效率。