Hybrid Proximal-Point Methods for Systems of Generalized Equilibrium Problems and Maximal Monotone Operators in Banach Spaces

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Abstract: In this paper, by using Bregman’s technique, we introduce and study the hybrid proximal-point methods for finding a common element of the set of solutions to a system of generalized equilibrium Problems and zeros of a finite family of maximal monotone operators in reflexive Banach spaces. Strong convergence results of the proposed hybrid proximal-point algorithms are also established under some suitable conditions. As applications, the existence of solutions for a class of bilevel variational inequalities are established and some numerical examples are reported.

WSEAS Transactions on Mathematics, ISSN / E-ISSN: 1109-2769 / 2224-2880, Volume 13, 2014, Art. #25

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Jiawei Chen, Zhongping Wan, Yeol Je Cho, Shih-Sen Chang, "Hybrid Proximal-Point Methods for Systems of Generalized Equilibrium Problems and Maximal Monotone Operators in Banach Spaces," WSEAS Transactions on Mathematics, vol. 13, pp. 256-270, 2014, DOI:
Jiawei Chen, Zhongping Wan, Yeol Je Cho, Shih-Sen Chang. Hybrid Proximal-Point Methods for Systems of Generalized Equilibrium Problems and Maximal Monotone Operators in Banach Spaces. WSEAS Transactions on Mathematics. 2014;13:256-270.
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