Clifford-Valued Distributed Optimization Based on Recurrent Neural Networks

Zicong Xia; Yang Liu; Kit Ian Kou; Jun Wang

doi:10.1109/TNNLS.2021.3139865

Clifford-Valued Distributed Optimization Based on Recurrent Neural Networks

Zicong Xia
, Yang Liu^*
, Kit Ian Kou
, Jun Wang^*

^*Corresponding author for this work

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

44 Citations (Scopus)

Abstract

In this paper, we address the Clifford-valued distributed optimization subject to linear equality and inequality constraints. The objective function of the optimization problems is composed of the sum of convex functions defined in the Clifford domain. Based on the generalized Clifford gradient, a system of multiple Clifford-valued recurrent neural networks (RNNs) is proposed for solving the distributed optimization problems. Each Clifford-valued RNN minimizes a local objective function individually, with local interactions with others. The convergence of the neural system is rigorously proved based on the Lyapunov theory. Two illustrative examples are delineated to demonstrate the viability of the results in this article.

Original language	English
Pages (from-to)	7248-7259
Number of pages	12
Journal	IEEE Transactions on Neural Networks and Learning Systems
Volume	34
Issue number	10
Online published	14 Jan 2022
DOIs	https://doi.org/10.1109/TNNLS.2021.3139865
Publication status	Published - Oct 2023

Funding

This work was supported in part by the National Natural Science Foundation of China under Grant 62173308, in part by the Natural Science Foundation of Zhejiang Province of China under Grant LR20F030001 and Grant D19A010003, in part by the Research Grants Council of the Hong Kong Special Administrative Region of China under Grant 11202318 and Grant 11202019, and in part by the Science and Technology Planing Project of Guangzhou City of China under Grant 201907010043.

Research Keywords

Algebra
Artificial neural networks
Clifford-valued distributed optimization
Clifford-valued neural networks
Computer science
Lyapunov theory
Neurodynamics
Neurons
nonsmooth analysis
Optimization
Recurrent neural networks

RGC Funding Information

RGC-funded

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10.1109/TNNLS.2021.3139865

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@article{515943f04b344d76b8f4cda83de15358,

title = "Clifford-Valued Distributed Optimization Based on Recurrent Neural Networks",

abstract = "In this paper, we address the Clifford-valued distributed optimization subject to linear equality and inequality constraints. The objective function of the optimization problems is composed of the sum of convex functions defined in the Clifford domain. Based on the generalized Clifford gradient, a system of multiple Clifford-valued recurrent neural networks (RNNs) is proposed for solving the distributed optimization problems. Each Clifford-valued RNN minimizes a local objective function individually, with local interactions with others. The convergence of the neural system is rigorously proved based on the Lyapunov theory. Two illustrative examples are delineated to demonstrate the viability of the results in this article.",

keywords = "Algebra, Artificial neural networks, Clifford-valued distributed optimization, Clifford-valued neural networks, Computer science, Lyapunov theory, Neurodynamics, Neurons, nonsmooth analysis, Optimization, Recurrent neural networks",

author = "Zicong Xia and Yang Liu and Kou, \{Kit Ian\} and Jun Wang",

year = "2023",

month = oct,

doi = "10.1109/TNNLS.2021.3139865",

language = "English",

volume = "34",

pages = "7248--7259",

journal = "IEEE Transactions on Neural Networks and Learning Systems",

issn = "2162-237X",

publisher = "IEEE Computational Intelligence Society",

number = "10",

}

TY - JOUR

T1 - Clifford-Valued Distributed Optimization Based on Recurrent Neural Networks

AU - Xia, Zicong

AU - Liu, Yang

AU - Kou, Kit Ian

AU - Wang, Jun

PY - 2023/10

Y1 - 2023/10

N2 - In this paper, we address the Clifford-valued distributed optimization subject to linear equality and inequality constraints. The objective function of the optimization problems is composed of the sum of convex functions defined in the Clifford domain. Based on the generalized Clifford gradient, a system of multiple Clifford-valued recurrent neural networks (RNNs) is proposed for solving the distributed optimization problems. Each Clifford-valued RNN minimizes a local objective function individually, with local interactions with others. The convergence of the neural system is rigorously proved based on the Lyapunov theory. Two illustrative examples are delineated to demonstrate the viability of the results in this article.

AB - In this paper, we address the Clifford-valued distributed optimization subject to linear equality and inequality constraints. The objective function of the optimization problems is composed of the sum of convex functions defined in the Clifford domain. Based on the generalized Clifford gradient, a system of multiple Clifford-valued recurrent neural networks (RNNs) is proposed for solving the distributed optimization problems. Each Clifford-valued RNN minimizes a local objective function individually, with local interactions with others. The convergence of the neural system is rigorously proved based on the Lyapunov theory. Two illustrative examples are delineated to demonstrate the viability of the results in this article.

KW - Algebra

KW - Artificial neural networks

KW - Clifford-valued distributed optimization

KW - Clifford-valued neural networks

KW - Computer science

KW - Lyapunov theory

KW - Neurodynamics

KW - Neurons

KW - nonsmooth analysis

KW - Optimization

KW - Recurrent neural networks

UR - https://www.scopus.com/pages/publications/85123379284

UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-85123379284&origin=recordpage

U2 - 10.1109/TNNLS.2021.3139865

DO - 10.1109/TNNLS.2021.3139865

M3 - RGC 21 - Publication in refereed journal

SN - 2162-237X

VL - 34

SP - 7248

EP - 7259

JO - IEEE Transactions on Neural Networks and Learning Systems

JF - IEEE Transactions on Neural Networks and Learning Systems

IS - 10

ER -

Clifford-Valued Distributed Optimization Based on Recurrent Neural Networks

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Clifford-Valued Distributed Optimization Based on Recurrent Neural Networks

Abstract

Funding

Research Keywords

RGC Funding Information

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Other Access Options

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Other Files and Links

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GRF: Collaborative Neurodynamic Approaches to Portfolio Optimization

GRF: Intelligent Mission Planning and Tracking Control of Autonomous Surface Vehicles Based on Neural Computation

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