  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.
