A two-stage proximal algorithm for equilibrium problems in Hadamard spaces

Vedel, YI
1Semenov, VV
2Chabak, LM
1V.М. Glushkov Institute of Cybernetics of the NAS of Ukraine, Kyiv
2Hetman Petro Konashevich-Sahaydachniy Kyiv State Maritime Academy
Dopov. Nac. akad. nauk Ukr. 2020, 2:7-14
Section: Information Science and Cybernetics
Language: Russian

We consider the equilibrium problem in Hadamard spaces, which extends and unifies several problems in optimization, variational inequalities, fixed-point theory, and many other parts in nonlinear analysis. First, we give the necessary facts about Hadamard metric spaces and consider the statements of equilibrium problems associated with pseudo-monotone bifunctions with suitable conditions on the bifunctions in Hadamard spaces. Then, to approximate an equilibrium point, we consider the two-stage proximal algorithm for pseudo-monotone bifunctions. This algorithm is an analog of the previously studied two-stage algorithm for equilibrium problems in a Hilbert space. For Lipschitz-type pseudo-monotone bifunctions, a theorem on the weak convergence of sequences generated by the algorithm is proved.

Keywords: convergence., equilibrium problem, Hadamard space, pseudo-monotonicity, two-stage algorithm

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