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This paper proves that nonconvex quadratically constrained quadratic programs can be solved in polynomial time when their underlying graph is acyclic, provided the constraints satisfy a certain technical condition. We demonstrate this theory on optimal power-flow problems over tree networks.
The optimal power flow (OPF) problem is critical to power system operation but it is generally non-convex and therefore hard to solve. Recently, a sufficient condition has been found under which OPF has zero duality gap, which means that its solution can be computed efficiently by solving the convex dual problem. In this paper we simplify this sufficient(More)
—Several convex relaxations of the optimal power flow (OPF) problem have recently been developed using both bus injection models and branch flow models. In this paper, we prove relations among three convex relaxations: a semidefinite relaxation that computes a full matrix, a chordal relaxation based on a chordal extension of the network graph, and a(More)
—A competitive deregulated electricity market with increasingly active market players is foreseen to be the future of the electricity industry. In such settings, market power assessment is a primary concern. In this paper, we propose a novel functional approach for measuring long term market power that unifies a variety of popular market power indices.(More)
—Market power assessment is a prime concern when designing a deregulated electricity market. In this paper, we propose a new functional market power measure, termed transmission constrained network flow (TCNF), that unifies three large classes of long-term transmission constrained market power indices in the literature: residual supply based, network flow(More)
In this paper we quantify the total cost of an epidemic spreading through a social network, accounting for both the immunization and disease costs. Previous research has typically focused on determining the optimal strategy to limit the lifetime of a disease, without considering the cost of such strategies. In the large graph limit, we calculate the exact(More)
We consider the problem of finding the minimum sampling frequency required for N non-overlapping, bandpass signals. Recently a novel algorithm with a significantly reduced computational cost has been proposed for this problem. By exploiting a redundancy in this algorithm, we propose a method which further reduces the cost significantly. We use the fact that(More)
—We formulate the optimal placement, sizing and control of storage devices in a power network to minimize generation costs with the intent of load shifting. We assume deterministic demand, a linearized DC approximated power flow model and a fixed available storage budget. Our main result proves that when the generation costs are convex and nondecreasing,(More)