Sven Leyffer, Argonne National Laboratory
We are interested to solve topological design problems that arise in many important engineering and scientific applications, such additive manufacturing and the design of cloaking devices. We formulate these problems as massive mixed-integer PDE-constrained optimization (MIPDECO) problems, where each element in a finite-element discretization introduces a set of binary variables.. We show that despite their seemingly hopeless complexity, MIPDECOs can be solved efficiently (at a cost comparable to a single continuous PDE-constrained optimization solve). We discuss two classes of methods: rounding techniques that are shown to be asymptotically optimal, and trust-region techniques that converge under mesh refinement. We illustrate these solution techniques with examples from topology optimization.