IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v7y2019i2p119-d200278.html
   My bibliography  Save this article

Modified Relaxed CQ Iterative Algorithms for the Split Feasibility Problem

Author

Listed:
  • Xinglong Wang

    (College of Air Traffic Management, Civil Aviation University of China, Tianjin 300300, China)

  • Jing Zhao

    (College of Science, Civil Aviation University of China, Tianjin 300300, China)

  • Dingfang Hou

    (College of Science, Civil Aviation University of China, Tianjin 300300, China)

Abstract

The split feasibility problem models inverse problems arising from phase retrievals problems and intensity-modulated radiation therapy. For solving the split feasibility problem, Xu proposed a relaxed CQ algorithm that only involves projections onto half-spaces. In this paper, we use the dual variable to propose a new relaxed CQ iterative algorithm that generalizes Xu’s relaxed CQ algorithm in real Hilbert spaces. By using projections onto half-spaces instead of those onto closed convex sets, the proposed algorithm is implementable. Moreover, we present modified relaxed CQ algorithm with viscosity approximation method. Under suitable conditions, global weak and strong convergence of the proposed algorithms are proved. Some numerical experiments are also presented to illustrate the effectiveness of the proposed algorithms. Our results improve and extend the corresponding results of Xu and some others.

Suggested Citation

  • Xinglong Wang & Jing Zhao & Dingfang Hou, 2019. "Modified Relaxed CQ Iterative Algorithms for the Split Feasibility Problem," Mathematics, MDPI, vol. 7(2), pages 1-17, January.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:2:p:119-:d:200278
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/7/2/119/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/7/2/119/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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).
    2. Songnian He & Caiping Yang, 2013. "Solving the Variational Inequality Problem Defined on Intersection of Finite Level Sets," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-8, May.
    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. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. Billio, Monica & Casarin, Roberto & Osuntuyi, Anthony, 2016. "Efficient Gibbs sampling for Markov switching GARCH models," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 37-57.
    8. Jan Babecký & Fabrizio Coricelli & Roman Horváth, 2009. "Assessing Inflation Persistence: Micro Evidence on an Inflation Targeting Economy," Czech Journal of Economics and Finance (Finance a uver), Charles University Prague, Faculty of Social Sciences, vol. 59(2), pages 102-127, June.
    9. Lloyd, S. P., 2017. "Unconventional Monetary Policy and the Interest Rate Channel: Signalling and Portfolio Rebalancing," Cambridge Working Papers in Economics 1735, Faculty of Economics, University of Cambridge.
    10. Ichiro Fukunaga, 2007. "Imperfect Common Knowledge, Staggered Price Setting, and the Effects of Monetary Policy," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 39(7), pages 1711-1739, October.
    11. Albertazzi, Ugo & Gambacorta, Leonardo, 2009. "Bank profitability and the business cycle," Journal of Financial Stability, Elsevier, vol. 5(4), pages 393-409, December.
    12. Beck, Thorsten & Demirgüç-Kunt, Asli & Merrouche, Ouarda, 2013. "Islamic vs. conventional banking: Business model, efficiency and stability," Journal of Banking & Finance, Elsevier, vol. 37(2), pages 433-447.
    13. Jinho Bae & Chang-Jin Kim & Dong Kim, 2012. "The evolution of the monetary policy regimes in the U.S," Empirical Economics, Springer, vol. 43(2), pages 617-649, October.
    14. McMahon, Rob, 2020. "Co-developing digital inclusion policy and programming with indigenous partners: Interventions from Canada," Internet Policy Review: Journal on Internet Regulation, Alexander von Humboldt Institute for Internet and Society (HIIG), Berlin, vol. 9(2), pages 1-26.
    15. George W. Evans & Seppo Honkapohja, 2009. "Robust Learning Stability with Operational Monetary Policy Rules," Central Banking, Analysis, and Economic Policies Book Series, in: Klaus Schmidt-Hebbel & Carl E. Walsh & Norman Loayza (Series Editor) & Klaus Schmidt-Hebbel (Series (ed.),Monetary Policy under Uncertainty and Learning, edition 1, volume 13, chapter 5, pages 145-170, Central Bank of Chile.
    16. Lehtonen, Heikki & Kujala, Sanna, 2007. "Climate change impacts on crop risks and agricultural production in Finland," 101st Seminar, July 5-6, 2007, Berlin Germany 9259, European Association of Agricultural Economists.
    17. Michael Pomerleano, 2011. "Developing Regional Financial Markets – the Case of East Asia," Chapters, in: Ulrich Volz (ed.), Regional Integration, Economic Development and Global Governance, chapter 9, Edward Elgar Publishing.
    18. Gary Charness & Francesco Feri & Miguel A. Meléndez-Jiménez & Matthias Sutter, 2023. "An Experimental Study on the Effects of Communication, Credibility, and Clustering in Network Games," The Review of Economics and Statistics, MIT Press, vol. 105(6), pages 1530-1543, November.
    19. Kitsul, Yuriy & Wright, Jonathan H., 2013. "The economics of options-implied inflation probability density functions," Journal of Financial Economics, Elsevier, vol. 110(3), pages 696-711.
    20. Dieter Balkenborg & Rosemarie Nagel, 2016. "An Experiment on Forward vs. Backward Induction: How Fairness and Level k Reasoning Matter," German Economic Review, Verein für Socialpolitik, vol. 17(3), pages 378-408, August.

    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:7:y:2019:i:2:p:119-:d:200278. 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.