This article develops distributed synchronous and asynchronous algorithms for the large-scale semidefinite programming with diagonal constraints, which has wide applications in combinatorial optimization, image proces...
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This article develops distributed synchronous and asynchronous algorithms for the large-scale semidefinite programming with diagonal constraints, which has wide applications in combinatorial optimization, image processing, and community detection. The information of the semidefinite programming is allocated to multiple interconnected agents such that each agent aims to find a solution by communicating to its neighbors. Based on the low-rank property of solutions and the Burer-Monteiro factorization, we transform the original problem into a distributed optimization problem over unit spheres to reduce variable dimensions and ensure positive semidefiniteness without involving semidefinite projections, which are computationally expensive. For the distributed optimization problem, we propose distributed synchronous and asynchronous algorithms, both of which reduce computational burden and storage space compared with existing centralized algorithms. Specifically, the distributed synchronous algorithm almost surely escapes strict saddle points and converges to the set of optimal solutions to the optimization problem. In addition, the proposed distributed asynchronous algorithm allows communication delays and converges to critical points to the optimization problem under mild conditions. By applying the proposed algorithms to image segmentation, we illustrate the efficiency and convergence performance of the two proposed algorithms.
An increasing number of distributed generators will penetrate into the distribution power system in future smart grid, thus a centralized control strategy cannot effectively optimize the power loss problem in real-tim...
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An increasing number of distributed generators will penetrate into the distribution power system in future smart grid, thus a centralized control strategy cannot effectively optimize the power loss problem in real-time. This paper examines the idea of a fully distributed optimal power flow (OPF) approach, based on the alternating direction multiplier method, to optimize the power loss. The objectives are not only to effectively obtain the minimization of power loss, but also to analyze the effect of communication time-delay on optimization performance. Both synchronous and asynchronous iterative algorithms are proposed to solve the OPF problem. In addition, four different strategies are proposed to improve convergence speed when delay occurs. The proposed weighted autoregressive strategy can reduce the fluctuation effectively. In comparison with synchronous algorithm, simulation results show that the asynchronous algorithm has a better optimization result.
This paper considers both synchronous and asynchronous consensus algorithms with noisy measurements. For stochastic approximation based consensus algorithms, the existing convergence analysis with dynamic topologies h...
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This paper considers both synchronous and asynchronous consensus algorithms with noisy measurements. For stochastic approximation based consensus algorithms, the existing convergence analysis with dynamic topologies heavily relies on quadratic Lyapunov functions, whose existence, however, may be difficult to ensure for switching directed graphs. Our main contribution is to introduce a new analytical approach. We first show a fundamental role of ergodic backward products for mean square consensus in algorithms with additive noise. Subsequently, we develop ergodicity results for backward products of degenerating stochastic matrices converging to a 0-1 matrix via a discrete time dynamical system approach. These results complement the existing ergodic theory of stochastic matrices and provide an effective tool for analyzing consensus problems. Under a joint connectivity assumption, our approach may deal with switching topologies, delayed measurements and correlated noises, and it does not require the double stochasticity condition typically assumed for the existence of quadratic Lyapunov functions.
The goal of the sensor network localization problem is to determine positions of all sensor nodes in a network given certain pairwise noisy distance measurements and some anchor node positions. This paper describes a ...
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The goal of the sensor network localization problem is to determine positions of all sensor nodes in a network given certain pairwise noisy distance measurements and some anchor node positions. This paper describes a distributed localization algorithm based on second-order cone programming relaxation. We show that the sensor nodes can estimate their positions based on local information. Unlike previous approaches, we also consider the effect of inaccurate anchor positions. In the presence of anchor position errors, the localization is performed in three steps. First, the sensor nodes estimate their positions using information from their neighbors. In the second step, the anchors refine their positions using relative distance information exchanged with their neighbors and finally, the sensors refine their position estimates. We demonstrate the convergence of the algorithm numerically. Simulation study, for both uniform and irregular network topologies, illustrates the robustness of the algorithm to anchor position and distance estimation errors, and the performance gains achievable in terms of localization accuracy, problem size reduction and computational efficiency.
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