Customized algorithms for growing connected resistive networks

Abstract

Abstract: We consider the problem of adding edges to connected resistive networks in order to optimally enhance their performance. The performance is captured by the H 2 norm of the closed-loop network and the l 1 regularization is introduced as a means to promote sparsity of the controller graph Laplacian. The resulting optimal control problem can be cast as a semidefinite program and 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 two efficient customized algorithms for large-scale problems. Our customized algorithms are based on the proximal gradient method and the sequential quadratic approximation method. In the latter, the Newton direction is obtained using coordinate descent algorithm over the set of active variables. We provide comparison of these methods and show that both of them can be effectively employed to solve topology identification and optimal design problems for large-scale networks.