On simplifying the primal-dual method of multipliers

2016 ◽  
Author(s):  
Guoqiang Zhang ◽  
Richard Heusdens
Keyword(s):  
Dual Method ◽  
Method Of Multipliers ◽  
Primal Dual

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 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 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>

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