Convex optimization for optimal realization of material properties

We show how the best passive approximation to a given target material or structure can be found by convex optimization. The approach is based on a representation of positive real functions, where some of the parameters can be given physical relevance by comparison to low- and high-frequency asymptotics of the material or structure under study. A number of different optimization problems can be formulated, which generalizes previous approaches using sum rules.