We introduce a domain decomposition-based nonlinear preconditioned iteration for solving nonlinear, nonsmooth elliptic optimal control problems, with a nonlinear reaction term, $L^1$ regularization and box constraints on the control function. The method is obtained by applying semismooth Newton to the fixed-point equation of the parallel optimized Schwarz iteration. As a proof of concept, numerical experiments are performed on two subdomains, as well as on a multi-subdomain test case. The results show that it is possible to obtain substantial improvements in robustness and efficiency with the new method, relative to semismooth Newton applied directly to the full optimization problem, provided appropriate Robin parameters and a good continuation strategy are chosen.

翻译：我们引入了一种基于域分解法的非线性非线性、非线性椭圆顶最佳控制问题的迭代,非线性反应术语为1美元,正规化和控件功能的框限制为1美元。这种方法是通过对平行优化施瓦兹迭代的固定点方程应用半斯moth Newton获得的。作为概念的证明,对两个子域进行了数字实验,并对一个多子体试验案例进行了数字实验。结果显示,如果选择了适当的罗宾参数和良好的延续战略,则有可能以新的方法(相对于适用于完全优化问题的半斯mooth Newton)在稳健性和效率方面实现重大改进。