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Computational Analysis of Variational Inequalities Using Mean Extra-Gradient Approach

Author

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  • Tingting Cai

    (Key Laboratory of Modern Power System Simulation and Control & Renewable Energy Technology, Ministry of Education, Northeast Electric Power University, Jilin 132000, China
    Northeast Electric Power University and Nanchang University are the co-first affiliation of this paper.)

  • Dongmin Yu

    (School of Information Engineering, Nanchang University, Nanchang 330027, China
    Northeast Electric Power University and Nanchang University are the co-first affiliation of this paper.)

  • Huanan Liu

    (Key Laboratory of Modern Power System Simulation and Control & Renewable Energy Technology, Ministry of Education, Northeast Electric Power University, Jilin 132000, China
    Northeast Electric Power University and Nanchang University are the co-first affiliation of this paper.)

  • Fengkai Gao

    (Key Laboratory of Modern Power System Simulation and Control & Renewable Energy Technology, Ministry of Education, Northeast Electric Power University, Jilin 132000, China
    Northeast Electric Power University and Nanchang University are the co-first affiliation of this paper.)

Abstract

An improved variational inequality strategy for dealing with variational inequality in a Hilbert space is proposed in this article as an alternative; if Hilbert space is used as the domain of interest, the original extra-gradient method is proposed for resolving variational inequality. This improved variational inequality strategy can be used as a substitute for the original extra-gradient method in some situations. Mann’s mean value method, coupled with the widely used sub-gradient extra-gradient strategy, makes it possible to update all of the previous iterations in a single step, thus saving time and effort. All of this is made feasible via the use of Mann’s mean value technique in conjunction with the convex hull of all prior iterations of the algorithm. It is guaranteed that the mean value iteration will result in an acceptable resolution of a variational inequality issue as long as one or more of the criteria for the averaging matrix are fulfilled. Numerous experiments were performed in order to demonstrate the correctness of the theoretical conclusion obtained.

Suggested Citation

  • Tingting Cai & Dongmin Yu & Huanan Liu & Fengkai Gao, 2022. "Computational Analysis of Variational Inequalities Using Mean Extra-Gradient Approach," Mathematics, MDPI, vol. 10(13), pages 1-14, July.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:13:p:2318-:d:854485
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    References listed on IDEAS

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    1. Pattrawut Chansangiam, 2015. "A Survey on Operator Monotonicity, Operator Convexity, and Operator Means," International Journal of Analysis, Hindawi, vol. 2015, pages 1-8, November.
    2. Fan, Siyuan & Wang, Yu & Cao, Shengxian & Sun, Tianyi & Liu, Peng, 2021. "A novel method for analyzing the effect of dust accumulation on energy efficiency loss in photovoltaic (PV) system," Energy, Elsevier, vol. 234(C).
    3. Dongmin Yu & Zimeng Ma & Rijun Wang & Wen-Tsao Pan, 2022. "Efficient Smart Grid Load Balancing via Fog and Cloud Computing," Mathematical Problems in Engineering, Hindawi, vol. 2022, pages 1-11, May.
    4. Fengkai Gao & Dongmin Yu & Qiang Sheng, 2022. "Analytical Treatment of Unsteady Fluid Flow of Nonhomogeneous Nanofluids among Two Infinite Parallel Surfaces: Collocation Method-Based Study," Mathematics, MDPI, vol. 10(9), pages 1-13, May.
    5. Rapeepan Kraikaew & Satit Saejung, 2014. "Strong Convergence of the Halpern Subgradient Extragradient Method for Solving Variational Inequalities in Hilbert Spaces," Journal of Optimization Theory and Applications, Springer, vol. 163(2), pages 399-412, November.
    6. Y. Censor & A. Gibali & S. Reich, 2011. "The Subgradient Extragradient Method for Solving Variational Inequalities in Hilbert Space," Journal of Optimization Theory and Applications, Springer, vol. 148(2), pages 318-335, February.
    7. Dongmin Yu & Rijun Wang, 2022. "An Optimal Investigation of Convective Fluid Flow Suspended by Carbon Nanotubes and Thermal Radiation Impact," Mathematics, MDPI, vol. 10(9), pages 1-15, May.
    8. Zhenhao Zhang & Changchun Luo & Zhenpeng Zhao, 2020. "Application of probabilistic method in maximum tsunami height prediction considering stochastic seabed topography," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 104(3), pages 2511-2530, December.
    9. Fan, Siyuan & Wang, Yu & Cao, Shengxian & Zhao, Bo & Sun, Tianyi & Liu, Peng, 2022. "A deep residual neural network identification method for uneven dust accumulation on photovoltaic (PV) panels," Energy, Elsevier, vol. 239(PD).
    10. Kassay, Gabor & Kolumban, Jozsef & Pales, Zsolt, 2002. "Factorization of Minty and Stampacchia variational inequality systems," European Journal of Operational Research, Elsevier, vol. 143(2), pages 377-389, December.
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