Algorithms for approximating minimization problems in Hilbert spaces

Authors:
Yonghong Yao;Shin Min Kang;Yeong-Cheng Liou
Affiliations:
Department of Mathematics, Tianjin Polytechnic University, Tianjin 300160, China;Department of Mathematics and the RINS, Gyeongsang National University, Jinju 660-701, Republic of Korea;Department of Information Management, Cheng Shiu University, Kaohsiung 833, Taiwan
Venue:
Journal of Computational and Applied Mathematics
Year:
2011

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Abstract

In this paper, we study the following minimization problem minx@?Fix(S)@?@W@m2+12@?x@?^2-h(x), where B is a bounded linear operator, @m=0 is some constant, h is a potential function for @c@?f, Fix(T) is the set of fixed points of nonexpansive mapping S and @W is the solution set of an equilibrium problem. This paper introduces two new algorithms (one implicit and one explicit) that can be used to find the solution of the above minimization problem.