Two-Step Proximal Method for Equilibrium Problems in Hadamard spaces

Authors

  • Yana I. Vedel Faculty of Computer Science and Cybernetics, Taras Shevchenko National University of Kyiv, Kyiv, Ukraine
  • Vladimir V. Semenov Faculty of Computer Science and Cybernetics, Taras Shevchenko National University of Kyiv https://orcid.org/0000-0002-3280-8245
  • Kateryna M. Golubeva Faculty of Computer Science and Cybernetics, Taras Shevchenko National University of Kyiv, Kyiv, Ukraine

DOI:

https://doi.org/10.31713/MCIT.2020.05

Keywords:

Hadamard space, equilibrium problem, convexity, pseudo-monotonicity, two-step proximal algorithm, convergence

Abstract

We propose a novel two-step proximal method for solving equilibrium problems in Hadamard spaces. The equilibrium problem is very general in the sense that it includes as special cases many applied mathematical models such as: variational inequalities, optimization problems, saddle point problems, and Nash equilibrium point problems. The proposed algorithm is the analog of the two-step algorithm for solving the equilibrium problem in Hilbert spaces explored earlier. We prove the weak convergence of the sequence generated by the algorithm for pseudo-monotone bifunctions. Our results extend some known results in the literature for pseudo-monotone equilibrium problems.

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Published

2020-10-23

How to Cite

Vedel, Y. I., Semenov, V. V., & Golubeva, K. M. (2020). Two-Step Proximal Method for Equilibrium Problems in Hadamard spaces. Modeling, Control and Information Technologies, (4), 71–74. https://doi.org/10.31713/MCIT.2020.05

Issue

No. 4 (2020): Modeling, control and information technologies

Section

Mathematical, computer modeling and computational methods

License

All materials are distributed under the terms of the Creative Commons Attribution 4.0 International License, which allows others to distribute the work with attribution to the authorship of this work and the first publication in this journal.