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After a brief introduction to the field of Conic Optimization we
present an interesting application to the (robust) resistor network
topology design (RNTD) problem, where the goal is to design an electrical network containing resistors only such that the dissipation is minimal, given the
external current values at the nodes of the network and assuming that the conductance values satisfy some normalizing constraint.
We present a linear model for the single-current case and
semidefinite models for the multi-current and the robust RNTD
problem. All models are illustrated by examples. It is also shown that by using duality the size of some of these models can be reduced significantly.
