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창의적인 신지식 창출과 산업계와의 협력적 네트워크 구축

금주의 우수논문

SCI-E Article
Convergence analysis of the discrete consensus-based optimization algorithm with random batch interactions and heterogeneous noises
김도헌
  1. 성명
    김도헌
  2. 소속
    과학기술융합대학 응용수학과
  3. 캠퍼스
  4. 우수선정주
    2022년 08월 2째주
Author
김도헌 (Dept Appl Math) corresponding author;
Corresponding Author Info
Kim, D(해당 저자), Hanyang Univ, Dept Appl Math, Hanyangdaehak Ro 55, Ansan 15588, Gyeonggi Do, South Korea.
E-mail
이메일doheonkim@hanyang.ac.kr
Document Type
Article
Source
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES Volume:32 Issue:6 Pages:1071-1107 Published:2022
Times Cited
0
External Information
http://dx.doi.org/10.1142/S0218202522500245
Abstract
We present stochastic consensus and convergence of the discrete consensus-based optimization (CBO) algorithm with random batch interactions and heterogeneous external noises. Despite the wide applications and successful performance in many practical simulations, the convergence of the discrete CBO algorithm was not rigorously investigated in such a generality. In this work, we introduce a generalized discrete CBO algorithm with a weighted representative point and random batch interactions, and show that the proposed discrete CBO algorithm exhibits stochastic consensus and convergence toward the common equilibrium state exponentially fast under suitable assumptions on system parameters. For this, we recast the given CBO algorithm with random batch interactions as a discrete consensus model with a random switching network topology, and then we use the mixing property of interactions over sufficiently long time interval to derive stochastic consensus and convergence estimates in mean square and almost sure senses. Our proposed analysis significantly improves earlier works on the convergence analysis of CBO models with full batch interactions and homogeneous external noises.
Web of Science Categories
Mathematics, Applied
Funding
Catholic University of Korea, Research Fund, 2021; National Research Foundation of Korea [NRF2021R1G1A1008559, NRF-2020R1A2C3A01003881]; National Natural Science Foundation of China [12031013]; Shanghai Municipal Science and Technology Major Project [2021
Language
English
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