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Modified Inertial Hybrid and Shrinking Projection Algorithms for Solving Fixed Point Problems

Author

Listed:
  • Bing Tan

    (Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China)

  • Shanshan Xu

    (School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China)

  • Songxiao Li

    (Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China)

Abstract

In this paper, we introduce two modified inertial hybrid and shrinking projection algorithms for solving fixed point problems by combining the modified inertial Mann algorithm with the projection algorithm. We establish strong convergence theorems under certain suitable conditions. Finally, our algorithms are applied to convex feasibility problem, variational inequality problem, and location theory. The algorithms and results presented in this paper can summarize and unify corresponding results previously known in this field.

Suggested Citation

  • Bing Tan & Shanshan Xu & Songxiao Li, 2020. "Modified Inertial Hybrid and Shrinking Projection Algorithms for Solving Fixed Point Problems," Mathematics, MDPI, vol. 8(2), pages 1-12, February.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:2:p:236-:d:319861
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    References listed on IDEAS

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    1. Hong-Kun Xu, 2011. "Averaged Mappings and the Gradient-Projection Algorithm," Journal of Optimization Theory and Applications, Springer, vol. 150(2), pages 360-378, August.
    2. Luong Nguyen & Qamrul Hasan Ansari & Xiaolong Qin, 2020. "Linear conditioning, weak sharpness and finite convergence for equilibrium problems," Journal of Global Optimization, Springer, vol. 77(2), pages 405-424, June.
    3. Xiaolong Qin & Nguyen Thai An, 2019. "Smoothing algorithms for computing the projection onto a Minkowski sum of convex sets," Computational Optimization and Applications, Springer, vol. 74(3), pages 821-850, December.
    4. Nguyen Thai An & Nguyen Mau Nam & Xiaolong Qin, 2020. "Solving k-center problems involving sets based on optimization techniques," Journal of Global Optimization, Springer, vol. 76(1), pages 189-209, January.
    5. Q. L. Dong & Y. J. Cho & L. L. Zhong & Th. M. Rassias, 2018. "Inertial projection and contraction algorithms for variational inequalities," Journal of Global Optimization, Springer, vol. 70(3), pages 687-704, March.
    6. M. De la Sen & Mujahid Abbas, 2019. "On Best Proximity Results for a Generalized Modified Ishikawa’s Iterative Scheme Driven by Perturbed 2-Cyclic Like-Contractive Self-Maps in Uniformly Convex Banach Spaces," Journal of Mathematics, Hindawi, vol. 2019, pages 1-15, January.
    7. Boţ, Radu Ioan & Csetnek, Ernö Robert & Hendrich, Christopher, 2015. "Inertial Douglas–Rachford splitting for monotone inclusion problems," Applied Mathematics and Computation, Elsevier, vol. 256(C), pages 472-487.
    8. Songnian He & Qiao-Li Dong, 2018. "The Combination Projection Method for Solving Convex Feasibility Problems," Mathematics, MDPI, vol. 6(11), pages 1-13, November.
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    Cited by:

    1. Liya Liu & Xiaolong Qin & Jen-Chih Yao, 2020. "Strong Convergent Theorems Governed by Pseudo-Monotone Mappings," Mathematics, MDPI, vol. 8(8), pages 1-15, July.
    2. Timilehin O. Alakoya & Oluwatosin T. Mewomo & Yekini Shehu, 2022. "Strong convergence results for quasimonotone variational inequalities," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 95(2), pages 249-279, April.
    3. Bing Tan & Zheng Zhou & Songxiao Li, 2020. "Strong Convergence of Modified Inertial Mann Algorithms for Nonexpansive Mappings," Mathematics, MDPI, vol. 8(4), pages 1-11, March.

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