Computing multiple local minima of topology optimization problems with second-order methods

Topology optimisation finds the optimal material distribution of a fluid or solid in a domain, subject to PDE and volume constraints. There are many formulations and we opt for the density approach which results in a PDE, volume and inequality constrained, non-convex, infinite-dimensional optimisation problem without a priori knowledge of a good initial guess. Such problems can exhibit many local minima or even no minima. In practice, heuristics are used to obtain the global minimum, but these can fail even in the simplest of cases. In this talk, we will present an algorithm that solves such problems and systematically discovers as many of these local minima as possible along the way.