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.
翻译:我们提出了一种可分离方向乘子法(ADMM)来解决由逆向光刻问题导出的优化问题。这个优化问题的目标函数包括三个项:在晶片上成像和目标图案之间的误差、确保掩模是二进制的罚项和总变差正则化项。通过变量分离,我们为原始目标函数引入了一个增广拉格朗日量。在ADMM方法的框架下,将优化问题分为几个子问题。每个子问题都可以高效地解决。我们给出了该方法的收敛性分析。特别地,我们直接解决阈值截断成像函数,而不是解决关于sigmoid的子问题,该函数可以在解析上得到解决。我们还提供了许多数值实验来证明该方法的有效性。