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Yao, Yonghong; Liou, Yeong-Cheng

Composite algorithms for minimization over the solutions of equilibrium problems and fixed point problems. (English) Zbl 1203.49048

Abstr. Appl. Anal. 2010, Article ID 763506, 19 p. (2010).
Summary: The purpose of this paper is to solve the minimization problem of finding \(x^*\) such that \(x^*=\arg \min_{x\in \Gamma }\| x\|^2\), where \(\Gamma \) stands for the intersection set of the solution set of the equilibrium problem and the fixed points set of a nonexpansive mapping. We first present two new composite algorithms (one implicit and one explicit). Further, we prove that the proposed composite algorithms converge strongly to \(x^*\).

Cited in 3 Reviews
Cited in 9 Documents

MSC:

49M30 Other numerical methods in calculus of variations (MSC2010)

Keywords:

minimization problem; composite algorithms
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References:

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