Single Bregman projection method for solving variational inequalities in reflexive Banach spaces. (English) Zbl 1518.65056
Summary: In this paper, we introduce a single projection method with the Bregman distance technique for solving pseudomonotone variational inequalities in a real reflexive Banach space. The algorithm is designed such that its step size is determined by a self-adaptive process and there is only one computation of projection per iteration during implementation. This improves the convergence of the method and also avoids the need for choosing a suitable estimate of the Lipschitz constant of the cost function which is very difficult in practice. We prove some weak and strong convergence results under suitable conditions on the cost operator. We also provide some numerical experiments to illustrate the performance and efficiency of the proposed method.
MSC:
| 65J99 | Numerical analysis in abstract spaces |
| 47J25 | Iterative procedures involving nonlinear operators |
| 90C33 | Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming) |
Keywords:
variational inequalities; pseudomonotone mapping; self-adaptive step size; single projection method; Banach spacesReferences:
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