Projected subgradient algorithms on systems of equilibrium problems
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The paper proposes two parallel and cyclic algorithms for solving systems of equilibrium problems in Hilbert spaces. The algorithms combine two methods including the diagonal subgradient method and the projection method with parallel or cyclic computations. The obtained results can be considered as improvements over several previously known methods for systems of equilibrium problems in computational steps. The algorithms have also allowed to reduce several assumptions imposed on bifunctions. The strongly convergent theorems are established under suitable conditions.
KeywordsEquilibrium problem Monotone bifunction Pseudomonotone bifunction Diagonal subgradient method Projection method
The author would like to thank the Associate Editor and the anonymous referees for their valuable comments and suggestions which helped us very much in improving the original version of this paper. The guidance of Profs. P. K. Anh and L. D. Muu is also gratefully acknowledged.
- 17.Hieu, D.V.: Halpern subgradient extragradient method extended to equilibrium problems. Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales-Serie A: Matematicas (2016). doi: 10.1007/s13398-016-0328-9