An interior-point method for topology identification and optimal design of noisy networks

Sepideh Hassan-Moghaddam, Mihailo R. Jovanović

Published 2015-06-10Version 1

We consider the problem of optimal topology identification and design of the corresponding edge weights for stochastically-forced undirected networks. By introducing $\ell_1$-regularization into the optimal control formulation aimed at minimizing the steady-state variance amplification, this problem can be cast as a semidefinite program. Standard interior-point method solvers can be used to efficiently compute the optimal solution for small and medium size networks. In this paper, we develop a customized algorithm, based on infeasible primal-dual interior-point method, that is well-suited for large problems. The search direction is obtained using the direct method based on Cholesky factorization and an inexact iterative method based on the preconditioned conjugate gradients (PCG). We illustrate that both of these significantly outperform the general-purpose solvers and that the PCG method can solve the problems with hundreds of thousands of edges in the controller graph in several minutes, on a PC. We also exploit structure of connected resistive networks and demonstrate how additional edges can be systematically added in order to minimize the total effective resistance.