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

TitleA two-stage proximal algorithm for equilibrium problems in Hadamard spaces
Publication TypeJournal Article
Year of Publication2020
AuthorsVedel, YI, Semenov, VV, Chabak, LM
Abbreviated Key TitleDopov. Nac. akad. nauk Ukr.
SectionInformation Science and Cybernetics
Date Published2/2020

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.

Keywordsconvergence., equilibrium problem, Hadamard space, pseudo-monotonicity, two-stage algorithm

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