Linear convergence of a primal-dual algorithm for distributed interval optimization

Yinghui Wang; Jiuwei Wang; Xiaobo Song; Yanpeng Hu

doi:10.3934/era.2024041

Electronic Research Archive (Jan 2024)

Linear convergence of a primal-dual algorithm for distributed interval optimization

Yinghui Wang,
Jiuwei Wang,
Xiaobo Song ,
Yanpeng Hu

Affiliations

Yinghui Wang: 1. Key Laboratory of Knowledge Automation for Industrial Processes of Ministry of Education, School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing 100083, China 2. Beijing Engineering Research Center of Industrial Spectrum Imaging, School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing 100083, China
Jiuwei Wang: 3. University of Chinese Academy of Sciences, Beijing 100049, China 4. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
Xiaobo Song: 1. Key Laboratory of Knowledge Automation for Industrial Processes of Ministry of Education, School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing 100083, China 2. Beijing Engineering Research Center of Industrial Spectrum Imaging, School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing 100083, China
Yanpeng Hu: 1. Key Laboratory of Knowledge Automation for Industrial Processes of Ministry of Education, School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing 100083, China 2. Beijing Engineering Research Center of Industrial Spectrum Imaging, School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing 100083, China

DOI: https://doi.org/10.3934/era.2024041
Journal volume & issue: Vol. 32, no. 2
pp. 857 – 873

Abstract

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In this paper, we investigate a distributed interval optimization problem whose local functions are interval functions rather than scalar functions. Focusing on distributed interval optimization, this paper presents a distributed primal-dual algorithm. A criterion is introduced under which linear convergence to the Pareto solution of distributed interval optimization problems can be achieved without strong convexity. Lastly, a numerical simulation is presented to illustrate the linear convergence of the algorithm that has been proposed.

Published in Electronic Research Archive

ISSN: 2688-1594 (Online)
Publisher: AIMS Press
Country of publisher: United States
LCC subjects: Science: Mathematics; Technology: Technology (General): Industrial engineering. Management engineering: Applied mathematics. Quantitative methods
Website: https://www.aimspress.com/journal/era

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