Inertial extrapolation method with regularization for solving a new class of bilevel problem in real Hilbert spaces

• Francis Akutsah ^[1] ; Akindele Adebayo Mebawondu ^[1] ; Godwin Chidi Ugwunnadi ^[2] ; Paranjothi Pillay ^[1] ; Ojen Kumar Narain ^[1]
  1. [1] University of KwaZulu-Natal

     University of KwaZulu-Natal

     Ethekwini, Sudáfrica

     
  2. [2] Department of Mathematics, University of Eswatini; Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Pretoria
• Localización: SeMA Journal: Boletín de la Sociedad Española de Matemática Aplicada, ISSN-e 2254-3902, ISSN 2254-3902, Vol. 80, Nº. 3, 2023, págs. 503-524
• Idioma: inglés
• DOI: 10.1007/s40324-022-00293-2
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• Resumen

  • The purpose of this paper is to introduce a new class of bilevel problem in the frame work of a real Hilbert space. In addition, we introduce an inertial iterative method with a regularization term and we establish the strong convergence of the resulting methods under certain conditions imposed on regularization parameters. Finally, we present some numerical experiments to show the efficiency and applicability of the proposed method. The results obtained in this paper extend, generalize and improve several results in this direction.