Algorithm for the generalized Φ-strongly monotone mappings and application to the generalized convex optimization problem.

• Aibinu, M. O. ^[1] ; Mewomo, O. T. ^[1]
  1. [1] University of KwaZulu-Natal

     University of KwaZulu-Natal

     Ethekwini, Sudáfrica

     
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 38, Nº. 1, 2019, págs. 59-82
• Idioma: inglés
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• Resumen

  • Let E be a uniformly smooth and uniformly convex real Banach space and E∗ be its dual space. We consider a multivalued mapping A : E → 2E∗ which is bounded, generalized Φ-strongly monotone and such that for all t > 0, the range R(Jp+tA) = E∗, where Jp (p > 1) is the generalized duality mapping from E into 2E∗ . Suppose A−1(0) = ∅, we construct an algorithm which converges strongly to the solution of 0 ∈ Ax. The result is then applied to the generalized convex optimization problem.