Distributed optimal power flow (OPF) is a challenging non-linear, non-convex problem of central importance to the future power grid. Although many approaches are currently available in the literature, these require some form of central coordination to properly work. In this paper a fully distributed and robust algorithm for OPF is proposed which does not require any form of central coordination. The algorithm is based upon the alternating direction multiplier method (ADMM) in a form recently proposed by the author, which, in turn, builds upon the work of Schizas The approach is customized as a region-based optimization procedure, and it is tested in meaningful scenarios

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Abstract-In this paper we provide new compact integral expressions and associated simple asymptotic approximations for converse and achievability bounds in the finite blocklength regime. The chosen converse and random coding union bounds were taken from the recent work of Polyanskyi-Poor-Verdù, and are investigated under parallel AWGN channels, the AWGN channels, the BI-AWGN channel, and the BSC. The technique we use, which is a generalization of some recent results available from the literature, is to map the probabilities of interest into a Laplace integral, and then solve (or approximate) the integral by use of a steepest descent technique. The proposed results are particularly useful for short packet lengths, where the normal approximation may provide unreliable results.Index Terms-Channel capacity, Coding for noisy channels, Converse, Finite blocklength regime, Shannon theory.

The fractional Fourier transform (FRT) is an extension of the ordinary Fourier transform (FT). Applying the language of the unified FT, we develop FRT expressions for discrete and continuous signals, introducing a particular form of periodicity: chirp-periodicity. The FRT sampling theorem is derived as an extension of its ordinary counterpart

This paper presents a distributed approach to optimal power flow (OPF) in an electrical network, suitable for application in a future smart grid scenario where access to resource and control is decentralized. The non-convex OPF problem is solved by an augmented Lagrangian method, similar to the widely known ADMM algorithm, with the key distinction that penalty parameters are constantly increased. A (weak) assumption on local solver reliability is required to always ensure convergence. A certificate of convergence to a local optimum is available in the case of bounded penalty parameters. For moderate sized networks (up to 300 nodes, and even in the presence of a severe partition of the network), the approach guarantees a performance very close to the optimum, with an appreciably fast convergence speed. The generality of the approach makes it applicable to any (convex or non-convex) distributed optimization problem in networked form. In the comparison with the literature, mostly focused on convex SDP approximations, the chosen approach guarantees adherence to the reference problem, and it also requires a smaller local computational complexity effort.

We propose a distributed algorithm for sensor network localization, which is based upon a decomposition of the nonlinear nonconvex maximum likelihood (ML) localization problem. Decomposition and coordination are obtained by applying the alternating direction method of multipliers (ADMM), to provide a distributed, synchronous, and nonsequential algorithm. When penalty coefficients are locally increased under specific conditions, the algorithm is proved to converge irrespective of the chosen starting point. It is also shown to be fast and accurate, providing a performance, which is equivalent to that of a centralized solver. In the comparison with existing literature on distributed sensor network localization, the proposed method involves a much lighter local processing effort, an improved robustness in non-Gaussian scenarios, and a better adherence to the original problem

The paper investigates the possibility for giving a general definition of the fractional Fourier transform (FRT) for all signal classes [one-dimensional (1-D) and multidimensional, continuous and discrete, periodic and aperiodic]. Since the definition is based on the eigenfunctions of the ordinary Fourier transform (FT), the preliminary conditions is that the signal domain/periodicity be the same as the FT domain/periodicity. Within these classes, a general FRT definition is formulated, and the FRT properties are established. In addition, the multiplicity (which is intrinsic in a fractional operator) is clearly developed. The general definition is checked in the case in which the FRT is presently available and, moreover, to establish the FRT in new classes of signals

Abstract-We propose an efficient solution to peer-to-peer localization in a wireless sensor network which works in two stages. At the first stage the optimization problem is relaxed into a convex problem, given in the form recently proposed by Soares, Xavier, and Gomes. The convex problem is efficiently solved in a distributed way by an ADMM approach, which provides a significant improvement in speed with respect to the original solution. In the second stage, a soft transition to the original, non-convex, non relaxed formulation is applied in such a way to force the solution towards a local minimum. The algorithm is built in such a way to be fully distributed, and it is tested in meaningful situations, showing its effectiveness in localization accuracy and speed of convergence, as well as its inner robustness.