论文标题
乘法问题的乘数交替方向方法
An alternating direction method of multipliers for inverse lithography problem
论文作者
论文摘要
我们提出了一种交替的乘数方向方法（ADMM），以解决来自逆光刻的优化问题。优化问题的客观功能包括三个术语：晶圆和目标模式的成像之间的不匹配，确保掩码为二进制的惩罚项和总变化正则化项。通过可变分割，我们为原始目标功能引入了增强的拉格朗日。在ADMM方法的框架中，优化问题分为几个子问题。每个子问题都可以有效地解决。我们对所提出的方法进行收敛分析。特别是，我们没有求解有关sigmoid的子问题，而是直接求解可以通过分析求解的阈值截断成像函数。我们还提供了许多数值示例，以说明该方法的有效性。
We propose an alternating direction method of multipliers (ADMM) to solve an optimization problem stemming from inverse lithography. The objective functional of the optimization problem includes three terms: the misfit between the imaging on wafer and the target pattern, the penalty term which ensures the mask is binary and the total variation regularization term. By variable splitting, we introduce an augmented Lagrangian for the original objective functional. In the framework of ADMM method, the optimization problem is divided into several subproblems. Each of the subproblems can be solved efficiently. We give the convergence analysis of the proposed method. Specially, instead of solving the subproblem concerning sigmoid, we solve directly the threshold truncation imaging function which can be solved analytically. We also provide many numerical examples to illustrate the effectiveness of the method.
