IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i12p1365-d574073.html
   My bibliography  Save this article

Modified Inertial Forward–Backward Algorithm in Banach Spaces and Its Application

Author

Listed:
  • Yanlai Song

    (College of Science, Zhongyuan University of Technology, Zhengzhou 450007, China
    The authors contributed equally to this work.)

  • Mihai Postolache

    (Department of General Education, China Medical University, Taichung 40402, Taiwan
    Department of Interior Design, Asia University, Taichung 41354, Taiwan
    Gh. Mihoc-C. Iacob Institute of Mathematical Statistics and Applied Mathematics, Romanian Academy, 050711 Bucharest, Romania
    Department of Mathematics and Informatics, University “Politehnica” of Bucharest, 060042 Bucharest, Romania)

Abstract

In this paper, we present a new modified inertial forward–backward algorithm for finding a common solution of the quasi-variational inclusion problem and the variational inequality problem in a q -uniformly smooth Banach space. The proposed algorithm is based on descent, splitting and inertial ideas. Under suitable assumptions, we prove that the sequence generated by the iterative algorithm converges strongly to the unique solution of the abovementioned problems. Numerical examples are also given to demonstrate our results.

Suggested Citation

  • Yanlai Song & Mihai Postolache, 2021. "Modified Inertial Forward–Backward Algorithm in Banach Spaces and Its Application," Mathematics, MDPI, vol. 9(12), pages 1-17, June.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:12:p:1365-:d:574073
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/12/1365/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/12/1365/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Yanlai Song & Luchuan Ceng, 2013. "A general iteration scheme for variational inequality problem and common fixed point problems of nonexpansive mappings in q-uniformly smooth Banach spaces," Journal of Global Optimization, Springer, vol. 57(4), pages 1327-1348, December.
    2. Genaro López & Victoria Martín-Márquez & Fenghui Wang & Hong-Kun Xu, 2012. "Forward-Backward Splitting Methods for Accretive Operators in Banach Spaces," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-25, July.
    3. R. T. Rockafellar, 1976. "Augmented Lagrangians and Applications of the Proximal Point Algorithm in Convex Programming," Mathematics of Operations Research, INFORMS, vol. 1(2), pages 97-116, May.
    4. Unknown, 2005. "Forward," 2005 Conference: Slovenia in the EU - Challenges for Agriculture, Food Science and Rural Affairs, November 10-11, 2005, Moravske Toplice, Slovenia 183804, Slovenian Association of Agricultural Economists (DAES).
    5. Zhangsong Yao & Yan-Kuen Wu & Ching-Feng Wen & Jen-Chih Yao, 2021. "Strong Convergence Analysis of Iterative Algorithms for Solving Variational Inclusions and Fixed-Point Problems of Pseudocontractive Operators," Journal of Mathematics, Hindawi, vol. 2021, pages 1-7, April.
    6. Yao, Yonghong & Cho, Yeol Je & Liou, Yeong-Cheng, 2011. "Algorithms of common solutions for variational inclusions, mixed equilibrium problems and fixed point problems," European Journal of Operational Research, Elsevier, vol. 212(2), pages 242-250, July.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Nattakarn Kaewyong & Kanokwan Sitthithakerngkiet, 2021. "Modified Tseng’s Method with Inertial Viscosity Type for Solving Inclusion Problems and Its Application to Image Restoration Problems," Mathematics, MDPI, vol. 9(10), pages 1-15, May.
    2. Lu-Chuan Ceng & Meijuan Shang, 2019. "Generalized Mann Viscosity Implicit Rules for Solving Systems of Variational Inequalities with Constraints of Variational Inclusions and Fixed Point Problems," Mathematics, MDPI, vol. 7(10), pages 1-18, October.
    3. Yuan Shen & Hongyong Wang, 2016. "New Augmented Lagrangian-Based Proximal Point Algorithm for Convex Optimization with Equality Constraints," Journal of Optimization Theory and Applications, Springer, vol. 171(1), pages 251-261, October.
    4. Li Wei & Yingzi Shang & Ravi P. Agarwal, 2019. "New Inertial Forward-Backward Mid-Point Methods for Sum of Infinitely Many Accretive Mappings, Variational Inequalities, and Applications," Mathematics, MDPI, vol. 7(5), pages 1-19, May.
    5. Adamu, A. & Kitkuan, D. & Padcharoen, A. & Chidume, C.E. & Kumam, P., 2022. "Inertial viscosity-type iterative method for solving inclusion problems with applications," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 194(C), pages 445-459.
    6. Yixuan Yang & Yuchao Tang & Chuanxi Zhu, 2019. "Iterative Methods for Computing the Resolvent of Composed Operators in Hilbert Spaces," Mathematics, MDPI, vol. 7(2), pages 1-16, February.
    7. Yekini Shehu & Aviv Gibali, 2020. "Inertial Krasnoselskii–Mann Method in Banach Spaces," Mathematics, MDPI, vol. 8(4), pages 1-13, April.
    8. Pilar Lopez-Llompart & G. Mathias Kondolf, 2016. "Encroachments in floodways of the Mississippi River and Tributaries Project," 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. 81(1), pages 513-542, March.
    9. Cheng, Jianquan & Bertolini, Luca, 2013. "Measuring urban job accessibility with distance decay, competition and diversity," Journal of Transport Geography, Elsevier, vol. 30(C), pages 100-109.
    10. M. De Donno & M. Pratelli, 2006. "A theory of stochastic integration for bond markets," Papers math/0602532, arXiv.org.
    11. Prilly Oktoviany & Robert Knobloch & Ralf Korn, 2021. "A machine learning-based price state prediction model for agricultural commodities using external factors," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 44(2), pages 1063-1085, December.
    12. Michelle Sheran Sylvester, 2007. "The Career and Family Choices of Women: A Dynamic Analysis of Labor Force Participation, Schooling, Marriage and Fertility Decisions," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 10(3), pages 367-399, July.
    13. Henrekson, Magnus & Johansson, Dan, 2010. "Firm Growth, Institutions and Structural Transformation," Ratio Working Papers 150, The Ratio Institute.
    14. Karen K. Lewis, 2011. "Global Asset Pricing," Annual Review of Financial Economics, Annual Reviews, vol. 3(1), pages 435-466, December.
    15. DAVID M. BLAU & WILBERT van der KLAAUW, 2013. "What Determines Family Structure?," Economic Inquiry, Western Economic Association International, vol. 51(1), pages 579-604, January.
    16. Panagiota DIONYSOPOULOU & Georgios SVARNIAS & Theodore PAPAILIAS, 2021. "Total Quality Management In Public Sector, Case Study: Customs Service," Regional Science Inquiry, Hellenic Association of Regional Scientists, vol. 0(1), pages 153-168, June.
    17. Mauricio Romero Sicre, 2020. "On the complexity of a hybrid proximal extragradient projective method for solving monotone inclusion problems," Computational Optimization and Applications, Springer, vol. 76(3), pages 991-1019, July.
    18. Afanasyev, Dmitriy O. & Fedorova, Elena A. & Popov, Viktor U., 2015. "Fine structure of the price–demand relationship in the electricity market: Multi-scale correlation analysis," Energy Economics, Elsevier, vol. 51(C), pages 215-226.
    19. Peter Viggo Jakobsen, 2009. "Small States, Big Influence: The Overlooked Nordic Influence on the Civilian ESDP," Journal of Common Market Studies, Wiley Blackwell, vol. 47(1), pages 81-102, January.
    20. Julie Holland Mortimer, 2007. "Price Discrimination, Copyright Law, and Technological Innovation: Evidence from the Introduction of DVDs," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 122(3), pages 1307-1350.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:9:y:2021:i:12:p:1365-:d:574073. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.