In this work, a class of parabolic economic optimal control problems is considered. These problems are characterized by pointwise state constraints regularized by a parameter, which transforms the pure state constraints in mixed control-state ones. However, the convergence of classical (semismooth) Newton methods deteriorates for decreasing values of the regularization parameter. To tackle this problem, a nonlinear preconditioner is introduced. This is based on an overlapping optimized waveform-relaxation method characterized by Robin transmission conditions. Numerical experiments show that appropriate choices of the overlap and of the Robin parameter lead to a preconditioned Newton method with a robust convergence against the state constraints regularization parameter.

翻译：在这项工作中,考虑了一系列的抛物线经济最佳控制问题,这些问题的特点是,以参数为常规的点度限制,这改变了混合控制状态的纯状态限制。然而,古典(semismouth)牛顿方法的趋同使得正规化参数的值下降而恶化。为了解决这一问题,引入了非线性先决条件。这是基于以Robin传输条件为特点的重叠的优化波形放松法。数字实验表明,对重叠和罗宾参数的适当选择导致一种先决条件的牛顿方法,与国家制约规范参数形成有力的趋同。