Primal–dual Newton interior point methods in shape and topology optimization

We consider non‐linear minimization problems with both equality and inequality constraints on the state variables and design parameters as they typically arise in shape and topology optimization. In particular, the state variables are subject to a partial differential equation or systems of partial differential equations describing the operating behaviour of the device or system to be optimized. For the numerical solution of the appropriately discretized problems we emphasize the use of all‐in‐one approaches where the numerical solution of the discretized state equations is an integral part of the optimization routine. Such an approach is given by primal–dual Newton interior point methods which we present combined with a suitable steplength selection and a watchdog strategy for convergence monitoring. As applications, we deal with the topology optimization of electric drives for high power electromotors and with the shape optimization of biotemplated microcellular biomorphic ceramics based on homogenization modelling. Copyright © 2004 John Wiley & Sons, Ltd.