Abstract
We introduce and analyze two modified subgradient extragradient methods with adaptive step sizes for solving variational inequality problems governed by pseudomonotone and Lipschitz continuous operators in real Hilbert spaces. For the first algorithm, a sufficient condition for weak convergence is established under pseudomonotonicity and Lipschitz continuity assumptions, with a possibly unknown Lipschitz constant. A sufficient condition for weak convergence for the second algorithm is proved under pseudomonotonicity and uniform continuity assumptions. We also establish an R-linear rate of convergence under strong pseudomonotonicity and Lipschitz continuity hypotheses regarding the variational inequality operator. Finally, we present several numerical computational experiments which involve a comparison of our proposed algorithms with other algorithms in some real-life applications.
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Thong, D.V., Reich, S., Shehu, Y. et al. Novel projection methods for solving variational inequality problems and applications. Numer Algor 93, 1105–1135 (2023). https://doi.org/10.1007/s11075-022-01457-x
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DOI: https://doi.org/10.1007/s11075-022-01457-x
Keywords
- Convergence rate
- Nash-Cournot oligopolistic equilibrium model
- Projection method
- Pseudomonotone mapping
- Tomography reconstruction model
- Variational inequality