A new hybrid method for solving variational inequalities

Authors

  • Yu.V. Malitsky
  • V.V. Semenov

DOI:

https://doi.org/10.15407/dopovidi2014.04.049

Keywords:

hybrid method, variational inequalities

Abstract

We introduce a new method for solving variational inequalities with monotone and Lipschitz-continuous operators acting in a Hilbert space. The iterative process based on the well-known projection method and the hybrid (or outer approximations) method. However, we do not use an extrapolation step in the projection method. The absence of one projection in our method is explained by a slightly different choice of sets in the hybrid method. We prove the strong convergence of the sequences generated by our method.

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References

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Published

17.02.2025

How to Cite

Malitsky, Y., & Semenov, V. (2025). A new hybrid method for solving variational inequalities . Reports of the National Academy of Sciences of Ukraine, (4), 49–55. https://doi.org/10.15407/dopovidi2014.04.049

Issue

No. 4 (2014): Reports of the National Academy of Sciences of Ukraine

Section

Information Science and Cybernetics

License

Copyright (c) 2025 Reports of the National Academy of Sciences of Ukraine

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This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

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