joint work with Lukas Pflug
A stochastic gradient method for the solution of structural optimization problems for which the objective function is given as an integral of a desired property over a continuous parameter set is presented. While the application of a quadrature rule leads to undesired local minima, the new stochastic gradient method does not rely on an approximation of the integral, requires only one state solution per iteration and utilizes gradients from previous iterations in an optimal way. Convergence theory and numerical examples including comparisons to the classical SG and SAG method are shown.
joint work with Jacek Gondzio
We focus on a semidefinite program arising in optimization of globally stable truss structures. These problems are known to be large-scale and very challenging to standard solution techniques. We solve the problems using a primal-dual interior point method, coupled with column generation procedure and warm-start strategy. The implementation of the algorithm extensively exploits the sparsity structure and low rank property of the involved matrices. We report on a solution of very large problems which otherwise would be prohibitively expensive for existing semidefinite programming solvers.
joint work with Michael Hintermüller
This talk is concerned with an adjoint-based topology optimization method for designing an electrical machine. In order to meet the requirements of real industrial applications, different objectives regarding energy efficiency, as well as mechanical robustness need to be addressed. The resulting optimization problem is challenging due to pointwise state constraints, which are tackled by a penalization approach. A line search type gradient descent scheme is presented for the numerical solution of the optimization problem, where the topological derivative serves as a descent direction.