A randomized incremental primal-dual method for decentralized consensus optimization

2019 ◽  
pp. 1-25
Author(s):  
Chenxi Chen ◽  
Yunmei Chen ◽  
Xiaojing Ye
Keyword(s):  
Convergence Rates ◽  
Optimization Problems ◽  
Dual Method ◽  
Selection Strategy ◽  
Consensus Algorithms ◽  
Uniform Sampling ◽  
Primal Dual ◽  
Multi Agent ◽  
Dual Variables ◽  
Consensus Optimization

We consider a class of convex decentralized consensus optimization problems over connected multi-agent networks. Each agent in the network holds its local objective function privately, and can only communicate with its directly connected agents during the computation to find the minimizer of the sum of all objective functions. We propose a randomized incremental primal-dual method to solve this problem, where the dual variable over the network in each iteration is only updated at a randomly selected node, whereas the dual variables elsewhere remain the same as in the previous iteration. Thus, the communication only occurs in the neighborhood of the selected node in each iteration and hence can greatly reduce the chance of communication delay and failure in the standard fully synchronized consensus algorithms. We provide comprehensive convergence analysis including convergence rates of the primal residual and consensus error of the proposed algorithm, and conduct numerical experiments to show its performance using both uniform sampling and important sampling as node selection strategy.

Multi-agent energy management of smart islands using primal-dual method of multipliers

Energy ◽  
2020 ◽  
Vol 208 ◽  
pp. 118306 ◽  
Author(s):  
Mohamed A. Mohamed ◽  
Tao Jin ◽  
Wencong Su
Keyword(s):  
Energy Management ◽  
Dual Method ◽  
Method Of Multipliers ◽  
Primal Dual ◽  
Multi Agent

scholarly journals A New Homotopy Proximal Variable-Metric Framework for Composite Convex Minimization

2021 ◽  
Author(s):  
Quoc Tran-Dinh ◽  
Ling Liang ◽  
Kim-Chuan Toh
Keyword(s):  
Convergence Rates ◽  
Optimization Problems ◽  
Linear Convergence ◽  
Convex Minimization ◽  
Variable Metric ◽  
Complexity Bounds ◽  
Convex Problems ◽  
Convex Minimization Problems ◽  
Global Iteration ◽  
Primal Dual

This paper suggests two novel ideas to develop new proximal variable-metric methods for solving a class of composite convex optimization problems. The first idea is to utilize a new parameterization strategy of the optimality condition to design a class of homotopy proximal variable-metric algorithms that can achieve linear convergence and finite global iteration-complexity bounds. We identify at least three subclasses of convex problems in which our approach can apply to achieve linear convergence rates. The second idea is a new primal-dual-primal framework for implementing proximal Newton methods that has attractive computational features for a subclass of nonsmooth composite convex minimization problems. We specialize the proposed algorithm to solve a covariance estimation problem in order to demonstrate its computational advantages. Numerical experiments on the four concrete applications are given to illustrate the theoretical and computational advances of the new methods compared with other state-of-the-art algorithms.

scholarly journals On the Primal-Dual Method of Multipliers and its Applications

2021 ◽  
Author(s):  
◽  
Matthew O'Connor
Keyword(s):  
Sensor Networks ◽  
Communication Systems ◽  
Optimization Problems ◽  
Function Optimization ◽  
Digital Data ◽  
Dual Method ◽  
Small Scale ◽  
Method Of Multipliers ◽  
Fusion Algorithm ◽  
Primal Dual

<p>With ever growing sources of digital data and the reductions in cost of small-scale wireless processing nodes, equipped with various sensors, microprocessors, and communication systems, we are seeing an increasing need for efficient distributed processing algorithms and techniques. This thesis focuses on the Primal-Dual Method of Multipliers (PDMM) as it applies to wireless sensor networks, and develops new algorithms based on PDMM more appropriate for the limitations on processing power, battery life, and memory that these devices suffer from. We develop FS-PDMM and QA-PDMM that greatly improve the efficiency of local node computations when dealing with regularized optimization problems and smooth cost function optimization problems, respectively. We combine these approaches to form the FSQA-PDMM algorithm that may be applied to problems with smooth cost functions and non-smooth regularization functions. Additionally, these three methods often eliminate the need for numerical optimization packages, reducing the memory cost on our nodes. We present the FT-PDMM algorithm for finite-time convergence of quadratic consensus problems, reducing the number of in-network iterations required for network convergence. Finally, we present two signal processing applications that benefit from our theoretical work: a distributed sparse near-field acoustic beamformer; and a distributed image fusion algorithm for use in imaging arrays. Simulated experiments confirm the benefit of our approaches, and demonstrate the computational gains to be made by tailoring our techniques towards sensor networks.</p>

scholarly journals On the Primal-Dual Method of Multipliers and its Applications

2021 ◽  
Author(s):  
◽  
Matthew O'Connor
Keyword(s):  
Sensor Networks ◽  
Communication Systems ◽  
Optimization Problems ◽  
Function Optimization ◽  
Digital Data ◽  
Dual Method ◽  
Small Scale ◽  
Method Of Multipliers ◽  
Fusion Algorithm ◽  
Primal Dual

<p>With ever growing sources of digital data and the reductions in cost of small-scale wireless processing nodes, equipped with various sensors, microprocessors, and communication systems, we are seeing an increasing need for efficient distributed processing algorithms and techniques. This thesis focuses on the Primal-Dual Method of Multipliers (PDMM) as it applies to wireless sensor networks, and develops new algorithms based on PDMM more appropriate for the limitations on processing power, battery life, and memory that these devices suffer from. We develop FS-PDMM and QA-PDMM that greatly improve the efficiency of local node computations when dealing with regularized optimization problems and smooth cost function optimization problems, respectively. We combine these approaches to form the FSQA-PDMM algorithm that may be applied to problems with smooth cost functions and non-smooth regularization functions. Additionally, these three methods often eliminate the need for numerical optimization packages, reducing the memory cost on our nodes. We present the FT-PDMM algorithm for finite-time convergence of quadratic consensus problems, reducing the number of in-network iterations required for network convergence. Finally, we present two signal processing applications that benefit from our theoretical work: a distributed sparse near-field acoustic beamformer; and a distributed image fusion algorithm for use in imaging arrays. Simulated experiments confirm the benefit of our approaches, and demonstrate the computational gains to be made by tailoring our techniques towards sensor networks.</p>

scholarly journals Boltzmann Distributed Replicator Dynamics: Population Games in a Microgrid Context

Games ◽  
2021 ◽  
Vol 12 (1) ◽  
pp. 8
Author(s):  
Gustavo Chica-Pedraza ◽  
Eduardo Mojica-Nava ◽  
Ernesto Cadena-Muñoz
Keyword(s):  
Control Method ◽  
Optimization Problems ◽  
Replicator Dynamics ◽  
Boltzmann Distribution ◽  
Full Information ◽  
Multi Agent Systems ◽  
Q Learning ◽  
Population Games ◽  
Distributed Approach ◽  
Multi Agent

Multi-Agent Systems (MAS) have been used to solve several optimization problems in control systems. MAS allow understanding the interactions between agents and the complexity of the system, thus generating functional models that are closer to reality. However, these approaches assume that information between agents is always available, which means the employment of a full-information model. Some tendencies have been growing in importance to tackle scenarios where information constraints are relevant issues. In this sense, game theory approaches appear as a useful technique that use a strategy concept to analyze the interactions of the agents and achieve the maximization of agent outcomes. In this paper, we propose a distributed control method of learning that allows analyzing the effect of the exploration concept in MAS. The dynamics obtained use Q-learning from reinforcement learning as a way to include the concept of exploration into the classic exploration-less Replicator Dynamics equation. Then, the Boltzmann distribution is used to introduce the Boltzmann-Based Distributed Replicator Dynamics as a tool for controlling agents behaviors. This distributed approach can be used in several engineering applications, where communications constraints between agents are considered. The behavior of the proposed method is analyzed using a smart grid application for validation purposes. Results show that despite the lack of full information of the system, by controlling some parameters of the method, it has similar behavior to the traditional centralized approaches.

scholarly journals Search Patterns Based on Trajectories Extracted from the Response of Second-Order Systems

2021 ◽  
Vol 11 (8) ◽  
pp. 3430
Author(s):  
Erik Cuevas ◽  
Héctor Becerra ◽  
Héctor Escobar ◽  
Alberto Luque-Chang ◽  
Marco Pérez ◽  
...  
Keyword(s):  
Convergence Rates ◽  
Optimization Problems ◽  
Search Space ◽  
Second Order ◽  
Order System ◽  
Search Patterns ◽  
Multiple Behaviors ◽  
Complex Optimization ◽  
Second Order Systems ◽  
Order Algorithm

Recently, several new metaheuristic schemes have been introduced in the literature. Although all these approaches consider very different phenomena as metaphors, the search patterns used to explore the search space are very similar. On the other hand, second-order systems are models that present different temporal behaviors depending on the value of their parameters. Such temporal behaviors can be conceived as search patterns with multiple behaviors and simple configurations. In this paper, a set of new search patterns are introduced to explore the search space efficiently. They emulate the response of a second-order system. The proposed set of search patterns have been integrated as a complete search strategy, called Second-Order Algorithm (SOA), to obtain the global solution of complex optimization problems. To analyze the performance of the proposed scheme, it has been compared in a set of representative optimization problems, including multimodal, unimodal, and hybrid benchmark formulations. Numerical results demonstrate that the proposed SOA method exhibits remarkable performance in terms of accuracy and high convergence rates.

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