Weak convergence of iterative methods for solving quasimonotone variational inequalities. (English) Zbl 07342388
Summary: In this work, we introduce self-adaptive methods for solving variational inequalities with Lipschitz continuous and quasimonotone mapping(or Lipschitz continuous mapping without monotonicity) in real Hilbert space. Under suitable assumptions, the convergence of algorithms are established without the knowledge of the Lipschitz constant of the mapping. The results obtained in this paper extend some recent results in the literature. Some preliminary numerical experiments and comparisons are reported.
MSC:
| 47J20 | Variational and other types of inequalities involving nonlinear operators (general) |
| 90C25 | Convex programming |
| 90C30 | Nonlinear programming |
| 90C52 | Methods of reduced gradient type |
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