AN INERTIAL NON-MONOTONIC SELF-ADAPTIVE ITERATIVE ALGORITHM FOR SOLVING EQUILIBRIUM PROBLEMS

Creative Commons License

Rehman H. U., Kumam P., Shehu Y., Ozdemir M., Kumam W.

JOURNAL OF NONLINEAR AND VARIATIONAL ANALYSIS, cilt.6, sa.1, ss.51-67, 2022 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 6 Sayı: 1
  • Basım Tarihi: 2022
  • Doi Numarası: 10.23952/jnva.6.2022.1.04
  • Dergi Adı: JOURNAL OF NONLINEAR AND VARIATIONAL ANALYSIS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED)
  • Sayfa Sayıları: ss.51-67
  • Anahtar Kelimeler: Equilibrium problem, Inertial method, Lipschitz-type conditions, Non-monotonic stepsize rule, Strong convergence, SUBGRADIENT EXTRAGRADIENT METHOD, STRONG-CONVERGENCE, PROJECTION
  • Atatürk Üniversitesi Adresli: Evet

Özet

In this paper, we introduce a modification of the extragradient algorithm with a non-monotonic stepsize rule to solve equilibrium problems. This modification is based on the inertial subgradient technique. Under mild conditions, such as, the Lipschitz continuity and the monotonicity of a bifunction (including the pseudomonotonicity), the strong convergence of the proposed algorithm is established in a real Hilbert space. The proposed algorithm uses a non-monotonic stepsize rule based on the local bifunction information rather than its Lipschitz-type constants or other line search methods. We present various numerical examples, which illustrate the strong convergence of the algorithm.