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In this paper, we consider using total variation minimization to recover signals whose gradients have a sparse support, from a small number of measurements. We establish the proof for the performance guarantee of total variation (TV) minimization in recovering one-dimensional signal with sparse gradient support. This partially answers the open problem of proving the fidelity of total variation minimization...
In this paper, we consider the non-convex active power loss minimization problem. Under the existence of saddle points and certain mild conditions, we show that a solution to the active power loss minimization can be achieved by applying the gradient dynamics approach. An important feature of this approach is that it is naturally distributed, i.e., each bus in the network only requires the local information...
The Optimal Power Flow (OPF) problem is non-convex and, for generic network structures, is NP-hard. A recent flurry of work has explored the use of semidefinite relaxations to solve the OPF problem. For general network structures, however, this approach may fail to yield solutions that are physically meaningful, in the sense that they are high rank - precluding their efficient mapping back to the...
We develop a novel design framework for decentralized resource sharing among self-interested users, who adjust their resource usage levels to minimize the costs of resource usage (e.g. energy consumption or payment) while fulfilling minimum payoff (e.g. throughput) requirements. We model the users' interaction as a repeated resource sharing game with imperfect monitoring, which captures the following...
This paper studies the problem of data-adaptive representations for big, distributed data. It is assumed that a number of geographically-distributed, interconnected sites have massive local data and they are interested in collaboratively learning a low-dimensional geometric structure underlying these data. In contrast to some of the previous works on subspace representations, this paper focuses on...
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