A filtered sequential approximate optimization algorithm based on dual subproblems using an enhanced two-point diagonal quadratic approximation for structural optimization

Abstract

In this study, we propose a new filtered diagonal quadratic approximate (FDQA) algorithm adopting the concept of a nonlinear acceptance filter for enhancing convergence property of convex and separable approximations based on dual subproblems. The proposed nonlinear acceptance filter tests whether the current optimum point is acceptable or not. If the current optimum point is rejected by the filter, the inner iteration is conducted until an acceptable optimum point is found. We also propose several values to obtain a more conservative approximation in the inner iteration stage. To investigate the efficiency and robustness of the proposed algorithm, two benchmark numerical examples and a structural topology optimization problem are solved. From the numerical tests, the proposed FDQA algorithm is found to be robust by improving convergence ability without worsening efficiency. In case of the topology optimization problem of minimizing compliance subject to a volume constraint with penalization parameter of three, the proposed algorithm is found to well converge in a efficient manner while the other three competing algorithms do not converge in a maximum number of iterations specified.