Abstract
The feasibility of a hybrid PMOR-SDP approach, that combines semidefinite programming (SDP) and parametric model order reduction (PMOR) was investigated. When an optimization problem comprises of a linear objective and linear matrix inequality constraints, SDP provides an efficient algorithm for arriving at a globally optimum design. This is achieved by solving a linear systems of equations that simultaneously satisfies the optimality conditions of the primal and dual problems. Weight minimization of a structure subjected to frequency or buckling constraints is amenable to this approach. It is postulated that with the right choice of basis and sufficient reduction in the size of the system matrices defining the problem, the convergence of the SDP problem can be accelerated. To test this idea, the weight minimization of a 200-bar truss, subjected to a frequency constraint, was studied here owing the relative simplicity of the problem. The MOSEK solver was used to solve the linear SDP problem. It was found that the Krylov space containing the second moment provided the best basis set. However, the expected reduction in optimization time was not achieved as this approach did not preserve the sparse nature of the stiffness and mass matrices. Future work will study structure-preserving model order reduction to address this issue.
