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AC OPF in radial distribution networks - Part II: An augmented Lagrangian-based OPF algorithm, distributable via primal decomposition

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ELECTRIC POWER SYSTEMS RESEARCH 2017年第Sep.期150卷 24-35页

作者： Christakou, Konstantina Tomozei, Dan-Cristian Le Boudec, Jean-Yves Paolone, Mario Ecole Polytech Fed Lausanne Lab Commun & Applicat 2 CH-1015 Lausanne Switzerland Ecole Polytech Fed Lausanne Distributed Elect Syst Lab CH-1015 Lausanne Switzerland Cisco Syst Inc EPFL Innovat Pk Bldg E CH-1015 Lausanne Switzerland

In the first part of this two-part paper we show that the branch-flow convexification of the OPF problem is not exact and that the ADMM-based decomposition of the OPF fails to converge in specific scenarios. Therefore, there is a need to develop algorithms for the solution of the non-approximated OPF problem that remains inherently non-convex. To overcome the limitations of recent approaches for the solution of the OPF problem, we propose in this paper, a specific algorithm for the solution of a non-approximated, non-convex AC OPF problem in radial distribution systems. It is based on the method of multipliers, as well as on a primal decomposition of the OPF problem. We provide a centralized version, as well as a distributed asynchronous version of the algorithm. We show that the centralized OPF algorithm converges to a local minimum of the global OPF problem and that the distributed version of the algorithm converges to the same solution as the centralized one. Here, in this second part of the two-part paper, we provide the formulation of the proposed algorithm and we evaluate its performance by using both small-scale electrical networks, as well as a modified IEEE 13-node test feeder. (C) 2017 Elsevier B.V. All rights reserved.

关键词： OPF ADMM Decomposition methods Method of multipliers Convex relaxation Active distribution networks Distributed algorithms asynchronous algorithms

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A First-Passage Kinetic Monte Carlo algorithm for complex diffusion-reaction systems

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JOURNAL OF COMPUTATIONAL PHYSICS 2010年第9期229卷 3214-3236页

作者： Donev, Aleksandar Bulatov, Vasily V. Oppelstrup, Tomas Gilmer, George H. Sadigh, Babak Kalos, Malvin H. Lawrence Livermore Natl Lab Livermore CA 94551 USA Royal Inst Technol KTH S-10044 Stockholm Sweden

We develop an asynchronous event-driven First-Passage Kinetic Monte Carlo (FPKMC) algorithm for continuous time and space systems involving multiple diffusing and reacting species of spherical particles in two and three dimensions. The FPKMC algorithm presented here is based on the method introduced in Oppelstrup et al. [10] and is implemented in a robust and flexible framework. Unlike standard KMC algorithms such as the n-fold algorithm, FPKMC is most efficient at low densities where it replaces the many small hops needed for reactants to find each other with large first-passage hops sampled from exact time-dependent Green's functions, without sacrificing accuracy. We describe in detail the key components of the algorithm, including the event-loop and the sampling of first-passage probability distributions, and demonstrate the accuracy of the new method. We apply the FPKMC algorithm to the challenging problem of simulation of long-term irradiation of metals, relevant to the performance and aging of nuclear materials in current and future nuclear power plants. The problem of radiation damage spans many decades of time-scales, from picosecond spikes caused by primary cascades, to years of slow damage annealing and microstructure evolution. Our implementation of the FPKMC algorithm has been able to simulate the irradiation of a metal sample for durations that are orders of magnitude longer than any previous simulations using the standard Object KMC or more recent asynchronous algorithms. (C) 2010 Elsevier Inc. All rights reserved.

关键词： Kinetic Monte Carlo First-passage Diffusion-reaction asynchronous algorithms

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A Polyhedral Approximation Framework for Convex and Robust Distributed Optimization

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2014年第2期59卷 384-395页

作者： Buerger, Mathias Notarstefano, Giuseppe Allgoewer, Frank Univ Stuttgart Inst Syst Theory & Automat Control D-70550 Stuttgart Germany Univ Lecce Dept Engn I-73100 Lecce Italy

In this paper, we consider a general problem setup for a wide class of convex and robust distributed optimization problems in peer-to-peer networks. In this setup, convex constraint sets are distributed to the network processors who have to compute the optimizer of a linear cost function subject to the constraints. We propose a novel fully distributed and asynchronous algorithm, named cutting-plane consensus, to solve the problem, based on a polyhedral outer approximation of the constraint sets. Processors running the algorithm compute and exchange linear approximations of their locally feasible sets. Independently of the number of processors in the network, each processor stores only a small number of linear constraints, making the algorithm scalable to large networks. The cutting-plane consensus algorithm is presented and analyzed for the general framework. Specifically, we prove the correctness of the algorithm, and show its robustness against communication or processor failures. Then, the cutting-plane consensus algorithm is specified to three different classes of distributed optimization problems, namely 1) inequality constrained problems, 2) robust optimization problems, and 3) almost separable optimization problems. For each one of these problem classes we solve a concrete problem and present computational results. That is, we show how to solve: position estimation in wireless sensor networks, a distributed robust linear program, and a distributed microgrid control problem.

关键词： asynchronous algorithms distributed optimization dual decomposition robust optimization

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COMPUTATIONALLY EFFICIENT algorithms FOR ONLINE OPTIMIZATION OF MARKOV DECISION-PROCESSES

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AUTOMATICA 1992年第1期28卷 107-118页

作者： JALALI, A FERGUSON, MJ INRS-Télécommunications 3 Place du Commerce Ile Des Soeurs Verdun Québec Canada H3E 1H6

Iterative algorithms are proposed for on-line optimization of finite state Markov decision processes. The optimization criterion is the minimization of long-run average cost. The transition probabilities of the underlying Markov chain are assumed to depend on certain unknown parameters. The algorithms estimate the unknown parameters using a strongly consistent estimator, and use this estimate in place of the true parameter to generate a sequence of control policies which converge to an optimal policy. The main feature of the algorithms is that the updating step does not have to be carried out in all states at each iteration. At each iteration, the updating step may be performed in any number of states-as few as one-as long as all states are updated "often enough" as the number of iterations increases;in this sense the algorithms are asynchronous. The asynchronous nature of our algorithms allows us to update the costly states more often. As will be illustrated through simulation results, the asynchronism of our algorithms makes them feasible for on-line optimization.

关键词： DISTRIBUTED algorithms COMPUTATIONAL METHODS DYNAMIC PROGRAMMING ESTIMATION asynchronous algorithms

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Non-stationary parallel multisplitting algorithms for almost linear systems

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NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS 1999年第2期6卷 79-92页

作者： Arnal, J Migallón, V Penadés, J Univ Alicante Dept Ciencia Computac & Inteligencia Artificial E-03071 Alicante Spain

Non-stationary parallel multisplitting iterative methods are introduced for the solution of almost linear systems. A non-stationary parallel algorithm based on the AOR-type methods and its extension to asynchronous models are considered. Convergence properties of the synchronous and asynchronous versions of these methods are studied for M-matrices and H-matrices. Furthermore, computational results about these methods on a distributed memory multiprocessor, which illustrate the performance of the algorithms studied, are discussed. Copyright (C) 1999 John Wiley & Sons, Ltd.

关键词： almost linear systems non-stationary multisplitting methods asynchronous algorithms parallel implementation distributed memory

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The first approximated distributed algorithm for the Minimum Degree Spanning Tree problem on general graphs

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INTERNATIONAL JOURNAL OF FOUNDATIONS OF COMPUTER SCIENCE 2004年第3期15卷 507-516页

作者： Blin, L Butelle, F Univ Paris 13 CNRS UMR 7030 LIPN F-93430 Villetaneuse France

In this paper we present the first distributed algorithm on general graphs for the Minimum Degree Spanning Tree problem. The problem is NP-hard in sequential. Our algorithm give a Spanning Tree of a degree at most 1 from the optimal. The resulting distributed algorithm is asynchronous, it works for named asynchronous arbitrary networks and achieves O(\V\) time complexity and O(\V\ \E\) message complexity.

关键词： distributed algorithms spanning trees minimum degree spanning trees asynchronous algorithms

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Distributed Learning with Sparse Communications by Identification

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SIAM JOURNAL ON MATHEMATICS OF DATA SCIENCE 2021年第2期3卷 715-735页

作者： Grishchenko, Dmitry Iutzeler, Franck Malick, Jerome Amini, Massih-Reza Univ Grenoble Alpes F-38000 Grenoble France CNRS LJK F-38401 St Martin Dheres France

In distributed optimization for large-scale learning, a major performance limitation stems from the communications between the different entities. To the extent that computations are performed by workers on local data while a coordinator machine coordinates their updates to minimize a global loss, we present an asynchronous optimization algorithm that efficiently reduces the communications between the coordinator and workers. This reduction comes from a random sparsification of the local updates. We show that this algorithm converges linearly in the strongly convex case and also identifies optimal strongly sparse solutions. We further exploit this identification to propose an automatic dimension reduction, aptly sparsifying all exchanges between coordinator and workers.

关键词： optimization asynchronous algorithms structure-promoting regularization proximal algorithms

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Distributed asynchronous Relaxation Methods for Linear Network Flow Problems

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IFAC Proceedings Volumes 1987年第5期20卷 103-114页

作者： D.P. Bertsekas J. Eckstein Laboraton for Information and Decision Systems and Operations Research Center Massachusetts Institute of Technology Cambridge MA 02139. USA

We consider a recently proposed, massively parallelizable algorithm [3]- [5] for the minimum cost network flow problem. The algorithm solves a dual problem which is unconstrained, piecewise linear, and involves a dual variable for each node. At each iteration a single node is chosen, and its dual variable and incident arc flows are changed in an attempt to improve the dual cost, as in Gauss-Seidel relaxation methods. In a distributed implementation, each node is a processor adjusting its own dual variable on the basis of local information communicated by adjacent nodes. We show finite convergence of a totally asynchronous (chaotic), distributed version of the algorithm in which some processors compute faster than others, some processors communicate faster than others, and there can be arbitrarily large communication delays. When scaling is applied to the serial version of the algorithm, excellent polynomial complexity bounds can be obtained as first pointed out in [23], and fully established in [24], [25]. We provide an alternative scaling procedure, and we discuss some variations of the algorithm aimed at improving practical computational performance.

关键词： Network flows relaxation distributed algorithms complexity asynchronous algorithms

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asynchronous iterations in optimization: new sequence results and sharper algorithmic guarantees

The Journal of Machine Learning Research

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The Journal of Machine Learning Research 2023年第1期24卷 7496-7570页

作者： Hamid Reza Feyzmahdavian Mikael Johansson ABB Corporate Research Västerås Sweden Division of Decision and Control Systems KTH — Royal Institute of Technology Stockholm Sweden

We introduce novel convergence results for asynchronous iterations that appear in the analysis of parallel and distributed optimization algorithms. The results are simple to apply and give explicit estimates for how the degree of asynchrony impacts the convergence rates of the iterates. Our results shorten, streamline and strengthen existing convergence proofs for several asynchronous optimization methods and allow us to establish convergence guarantees for popular algorithms that were thus far lacking a complete theoretical understanding. Specifically, we use our results to derive better iteration complexity bounds for proximal incremental aggregated gradient methods, to obtain tighter guarantees depending on the average rather than maximum delay for the asynchronous stochastic gradient descent method, to provide less conservative analyses of the speedup conditions for asynchronous block-coordinate implementations of Krasnosel'skii-Mann iterations, and to quantify the convergence rates for totally asynchronous iterations under various assumptions on communication delays and update rates.

关键词： asynchronous algorithms parallel methods incremental methods coordinate descent stochastic gradient descent

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SUCAG: Stochastic Unbiased Curvature-aided Gradient Method for Distributed Optimization 57

SUCAG: Stochastic Unbiased Curvature-aided Gradient Method f...

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57th IEEE Conference on Decision and Control (CDC)

作者： Wai, Hoi-To Freris, Nikolaos M. Nedic, Angelia Scaglione, Anna Arizona State Univ Sch Elect Comp & Energy Engn Tempe AZ 85281 USA New York Univ Abu Dhabi Div Engn Abu Dhabi U Arab Emirates NYU Tandon Sch Engn Brooklyn NY USA

ISBN: (纸本)9781538613955

We propose and analyze a new stochastic gradient method, which we call Stochastic Unbiased Curvature-aided Gradient (SUCAG), for finite sum optimization problems. SUCAG constitutes an unbiased total gradient tracking technique that uses Hessian information to accelerate convergence. We analyze our method under the general asynchronous model of computation, in which each function is selected infinitely often with possibly unbounded (but sublinear) delay. For strongly convex problems, we establish linear convergence for the SUCAG method. When the initialization point is sufficiently close to the optimal solution, the established convergence rate is only dependent on the condition number of the problem, making it strictly faster than the known rate for the SAGA method. Furthermore, we describe a Markov-driven approach of implementing the SUCAG method in a distributed asynchronous multi-agent setting, via gossiping along a random walk on an undirected communication graph. We show that our analysis applies as long as the graph is connected and, notably, establishes an asymptotic linear convergence rate that is robust to the graph topology. Numerical results demonstrate the merits of our algorithm over existing methods.

关键词： Distributed optimization Incremental methods asynchronous algorithms Randomized algorithms Multi-agent systems Machine learning

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