Strong convergence theorem for a new Bregman extragradient method with a different line-search process for solving variational inequality problems in reflexive Banach spaces. (English) Zbl 1543.90287
Summary: In this paper, we introduce a new Bregman extragradient method with a different line-search process for solving variational inequality problems in reflexive Banach spaces. Precisely, we prove that the sequence generated by our proposed iterative algorithm converges strongly to an element of the solution sets of variational inequality problems. Moreover, some numerical examples are given to show the effectiveness of the proposed algorithm. The results obtained in this paper extend and improve many recent ones in the literature.
MSC:
| 90C33 | Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming) |
| 47H05 | Monotone operators and generalizations |
| 47J25 | Iterative procedures involving nonlinear operators |
| 47H10 | Fixed-point theorems |
| 65J15 | Numerical solutions to equations with nonlinear operators |
| 65K15 | Numerical methods for variational inequalities and related problems |
Keywords:
extragradient method; variational inequality; pseudomonotone operator; strong convergence; Banach spacesReferences:
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