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>

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

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.

scholarly journals Ad hoc microphone array beamforming using the primal-dual method of multipliers

2016 ◽  
Author(s):  
Vincent M. Tavakoli ◽  
Jesper R. Jensen ◽  
Richard Heusdens ◽  
Jacob Benesty ◽  
Mads G. Christensen
Keyword(s):  
Ad Hoc ◽  
Microphone Array ◽  
Dual Method ◽  
Method Of Multipliers ◽  
Primal Dual ◽  
Array Beamforming

scholarly journals On the Detection of a Non-Cooperative Beam Signal Based on Wireless Sensor Networks

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Guofeng Wei ◽  
Bangning Zhang ◽  
Guoru Ding ◽  
Bing Zhao ◽  
Kefeng Guo ◽  
...  
Keyword(s):  
Wireless Sensor Networks ◽  
Sensor Networks ◽  
Detection Probability ◽  
Communication Systems ◽  
Prior Information ◽  
Signal Strength ◽  
Energy Detection ◽  
Wireless Sensor ◽  
Fusion Algorithm ◽  
Beam Signal

With the extensive research of multiantenna technology, beamforming (BF) will play an important role in the future communication systems due to its high transmission gain and satisfying directivity. If we can detect the non-cooperative beams, it is of great significance in counter reconnaissance, beam tracking, and spectrum sensing of multiantenna transmitters. This paper investigates the wireless sensor networks (WSNs), which is used to detect the unknown non-cooperative beam signal. In order to perceive the presence of beam signals without the prior information, we first derive the detection probability based on the sensors’ received signal strength (RSS). Then, based on the strong directivity of the beam signal, we propose an improved “k rank” fusion algorithm by jointly exploiting the energy detection (ED) information and location information of the sensors. Finally, the beam detection performance of different fusion algorithms is compared in simulation, and we find that our proposed algorithm showed better detection probability and lower error probability. The simulation results verify the correctness and effectiveness of the proposed algorithm.

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