Advanced primal-dual interior-point method for the method of moving asymptotes

The Method of Moving Asymptotes (MMA) is one of the well-known optimization algorithms for topology optimization due to its stable numerical performance. Here, this paper simplifies the MMA algorithm by considering the features of topology optimization problem statements and presents a strategy to solve the necessary subproblems based on the primal-dual-interior-point method to further enhance numerical performance. A new scaling mechanism is also introduced to improve searching quality by utilizing the sensitivities of the original problems at the beginning of each MMA iteration. Numerical examples of solving both mathematical problems and topology optimization problems demonstrate the success of this method.