TY - JOUR
T1 - An Alternating Direction Method of Multipliers for Inverse Lithography Problem
AU - Chen , Junqing
AU - Liu , Haibo
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 3
SP - 820
EP - 846
PY - 2023
DA - 2023/08
SN - 16
DO - http://doi.org/10.4208/nmtma.OA-2022-0151
UR - https://global-sci.org/intro/article_detail/nmtma/21968.html
KW - Inverse lithography techniques, ADMM framework, total variation regularization.
AB - <p style="text-align: justify;">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.</p>