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A second-order dynamical system for equilibrium problems

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Abstract

We consider a second-order dynamical system for solving equilibrium problems in Hilbert spaces. Under mild conditions, we prove existence and uniqueness of strong global solution of the proposed dynamical system. We establish the exponential convergence of trajectories under strong pseudo-monotonicity and Lipschitz-type conditions. We then investigate a discrete version of the second-order dynamical system, which leads to a fixed point-type algorithm with inertial effect and relaxation. The linear convergence of this algorithm is established under suitable conditions on parameters. Finally, some numerical experiments are reported confirming the theoretical results.

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Acknowledgements

The authors are grateful to both anonymous referees for their constructive comments, which helped improve the presentation of this paper. The research of Le Van Vinh is funded by Van Lang University, Vietnam. Nam Van Tran thanks the support from Ho Chi Minh City University of Technology and Education.

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Authors and Affiliations

  1. Faculty of Basic Sciences, Van Lang University, Ho Chi Minh City, Vietnam

    Le Van Vinh

  2. Faculty of Applied Sciences, Ho Chi Minh City University of Technology and Education, Ho Chi Minh City, Vietnam

    Van Nam Tran

  3. Mathematical Sciences School, University of Southampton, SO17 1BJ, Southampton, UK

    Phan Tu Vuong

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  1. Le Van Vinh
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  2. Van Nam Tran
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  3. Phan Tu Vuong
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Correspondence to Van Nam Tran.

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Van Vinh, L., Tran, V.N. & Vuong, P.T. A second-order dynamical system for equilibrium problems. Numer Algor 91, 327–351 (2022). https://doi.org/10.1007/s11075-022-01264-4

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