Faculty Publications

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Author: search.filters.author.Borkar, V.S.Has files: No

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    (2010) Borkar, V.S.; Nair, J.; Sanketh, N.
    A scheme for consensus formation is considered wherein the value of a certain variable associated with the nodes of a network is fixed a priori for a prescribed set of K nodes, and allowed to propagate throughout the network through an averaging process that mimics a gossip algorithm. The objective is to find the best choice of these K nodes that will achieve the fastest convergence to consensus. This objective is captured by the Perron-Frobenius eigenvalue of the resultant sub-stochastic matrix, which then is the quantity one seeks to minimize. We propose an algorithm for this optimization problem, as well as a greedy scheme with some performance guarantees for a variant of the problem that seeks to minimize a simpler objective. Some other related formulations are also considered. ©2010 IEEE.
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    (Institute of Electrical and Electronics Engineers Inc., 2015) Borkar, V.S.; Karnik, A.; Nair, J.; Nalli, S.
    We consider a variant of the gossip algorithm wherein a controller can influence the values at a subset of nodes as well as the averaging weights. This leads to three optimization problems: (i) Optimal choice of nodes: a combinatorial optimization problem for which we propose a nonlinear programming relaxation as well as a greedy heuristic; (ii) Parametric optimization of weights: a non-convex optimization for which we propose an effective heuristic for a special case; (iii) Dynamic adjustment of weights: an optimal control problem. For the dynamic case, we note some empirically observed interesting critical phenomena for the uncontrolled case. © 1963-2012 IEEE.