Primal–Dual Fixed Point Algorithms Based on Adapted Metric for Distributed Optimization

Li, Huaqing; Zheng, Zuqing; Lü, Qingguo; Wang, Zheng; Gao, Lan; Wu, Guo–Cheng; Ji, Lianghao; Wang, Huiwei

doi:10.1109/tnnls.2021.3110295

Cited by 9 publications

(3 citation statements)

References 55 publications

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“…The learning algorithms in question may comprise a multitude of layers, potentially numbering in the hundreds. Several designs incorporate a layered structure consisting of an input, a secret, and an output, as indicated in [1]. Instances of artificial intelligence in operation can be observed in a diverse range of computer applications and structural blueprints.…”

Section: Introductionmentioning

confidence: 99%

Theoretical Analysis of the Brain and Artificial Intelligence

Pedro

2023

JRS

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Many articles have expounded on and defended the potential advantages of co-robotics (cobots), robotics, AI, and quantum computers in the domains of research and development, clinics, community health and virology. Numerous trailblazers in the domains of artificial intelligence, robotics, and quantum computing have been recognised for their groundbreaking concepts and principles. Among these luminaries are Richard Feynman, Kurt Godel, John Nash, Norbert Wiener, Alan Turing, John von Neumann, Vannevar Bush, and John McCarthy. Theorems formulated by Kurt Godel were misinterpreted by researchers who erroneously equated computer and brain paradigms. Godel himself had recognised this misinterpretation. The individual's commendation of the brain's supremacy over computational systems was met with disapprobation. This article delineates the diverse array of artificial intelligence techniques, frameworks, and programming languages that are developed by humans and can be employed in tandem with contemporary computational systems. These advancements facilitate advancements in the realm of electrons and quantum mechanics. The process of evolution has resulted in the development of neurons in various animal species, which rely on the flow of electrons to carry out their biological functions. The identification of mirror neurons represented a significant shift in the paradigm of neuroscience. The proposed paradigm shift towards the 'hall of mirror neurons' represents a potentially effective approach to studying, warranting further investigation. The aforementioned concepts are instrumental in advancing the field of artificial intelligence and in furthering research on the intricacies of the human brain.

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Section: Introductionmentioning

confidence: 99%

Theoretical Analysis of the Brain and Artificial Intelligence

Pedro

2023

JRS

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“…To endow more independence, time-varying and nonidentical step-sizes of each agent were studied. A primal-dual fixed-point algorithm with nonidentical step-sizes was proposed by Li [37] when the object function of each agent was twice differentiable and nonsmooth. Xin [32] also adopted nonidentical step-sizes in a directed network.…”

Section: Introductionmentioning

confidence: 99%

A Distributed Optimization Accelerated Algorithm with Uncoordinated Time-Varying Step-Sizes in an Undirected Network

et al. 2022

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In recent years, significant progress has been made in the field of distributed optimization algorithms. This study focused on the distributed convex optimization problem over an undirected network. The target was to minimize the average of all local objective functions known by each agent while each agent communicates necessary information only with its neighbors. Based on the state-of-the-art algorithm, we proposed a novel distributed optimization algorithm, when the objective function of each agent satisfies smoothness and strong convexity. Faster convergence can be attained by utilizing Nesterov and Heavy-ball accelerated methods simultaneously, making the algorithm widely applicable to many large-scale distributed tasks. Meanwhile, the step-sizes and accelerated momentum coefficients are designed as uncoordinate, time-varying, and nonidentical, which can make the algorithm adapt to a wide range of application scenarios. Under some necessary assumptions and conditions, through rigorous theoretical analysis, a linear convergence rate was achieved. Finally, the numerical experiments over a real dataset demonstrate the superiority and efficacy of the novel algorithm compared to similar algorithms.

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“…The agents interact with each other through communication links, and this communication occurs only among the neighboring agents. Under these conditions, the distributed methods can effectively solve the optimization problems common to sensor networks [ 3 ], economic dispatch [ 4 , 5 , 6 ], machine learning [ 7 , 8 ] and dynamic control [ 9 ].…”

Section: Introductionmentioning

confidence: 99%

Decentralized Primal-Dual Proximal Operator Algorithm for Constrained Nonsmooth Composite Optimization Problems over Networks

Feng

Ran

Meng

et al. 2022

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In this paper, we focus on the nonsmooth composite optimization problems over networks, which consist of a smooth term and a nonsmooth term. Both equality constraints and box constraints for the decision variables are also considered. Based on the multi-agent networks, the objective problems are split into a series of agents on which the problems can be solved in a decentralized manner. By establishing the Lagrange function of the problems, the first-order optimal condition is obtained in the primal-dual domain. Then, we propose a decentralized algorithm with the proximal operators. The proposed algorithm has uncoordinated stepsizes with respect to agents or edges, where no global parameters are involved. By constructing the compact form of the algorithm with operators, we complete the convergence analysis with the fixed-point theory. With the constrained quadratic programming problem, simulations verify the effectiveness of the proposed algorithm.

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Primal–Dual Fixed Point Algorithms Based on Adapted Metric for Distributed Optimization

Cited by 9 publications

References 55 publications

Theoretical Analysis of the Brain and Artificial Intelligence

Theoretical Analysis of the Brain and Artificial Intelligence

A Distributed Optimization Accelerated Algorithm with Uncoordinated Time-Varying Step-Sizes in an Undirected Network

Decentralized Primal-Dual Proximal Operator Algorithm for Constrained Nonsmooth Composite Optimization Problems over Networks

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