椭圆型最优控制问题中的L^(1,2)-方向稀疏

L^(1,2)-Directional Sparsity of Elliptic Optimal Control Problems

介绍一种带有L1,2-方向稀疏项的椭圆型最优控制问题,分析条纹稀疏模式,从理论角度研究该问题的一阶最优性条件。为解决不可微控制问题,基于广义微分,提出一个半光滑牛顿方法,将问题在泛函空间中进行表示和分析,并具有局部超线性收敛率。

The elliptic optimal control problems with L1,2-directional sparsity are introduced and the stripe sparse mode is analyzed. Emphatically,the first-order optimality conditions of the problem are studied from the theory angle. For solving the non-differentiable control problem,a semi-smooth Newton method based on the generalized differential is proposed,with which the problem can be stated and analyzed in the functional space and has local superlinear convergence rate.