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：我们提出了一种交替方向乘子法(ADMM)来求解由逆光刻问题衍生出的优化问题。该优化问题的目标泛函包含三项：晶圆成像与目标图案之间的失配、确保掩膜为二值的惩罚项以及全变差正则化项。通过变量分裂，我们为原始目标泛函引入了增广拉格朗日函数。在ADMM方法的框架下，优化问题被分解为若干子问题，每个子问题均可高效求解。我们给出了所提方法的收敛性分析。特别地，我们没有求解与sigmoid函数相关的子问题，而是直接求解阈值截断成像函数，该函数可解析求解。我们还提供了大量数值算例以说明该方法的有效性。