Abstract and Applied Analysis

Algorithmic Approach to a Minimization Problem

Yonghong Yao, Shin Min Kang, Yeong-Cheng Liou, and Zhitao Wu

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Abstract

We first construct an implicit algorithm for solving the minimization problem min x x , where Ω is the intersection set of the solution set of some equilibrium problem, the fixed points set of a nonexpansive mapping, and the solution set of some variational inequality. Further, we suggest an explicit algorithm by discretizing this implicit algorithm. We prove that the proposed implicit and explicit algorithms converge strongly to a solution of the above minimization problem.

Article information

Source
Abstr. Appl. Anal., Volume 2012 (2012), Article ID 310801, 17 pages.

Dates
First available in Project Euclid: 28 March 2013

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1364475806

Digital Object Identifier
doi:10.1155/2012/310801

Mathematical Reviews number (MathSciNet)
MR2947721

Zentralblatt MATH identifier
1248.49045

Citation

Yao, Yonghong; Kang, Shin Min; Liou, Yeong-Cheng; Wu, Zhitao. Algorithmic Approach to a Minimization Problem. Abstr. Appl. Anal. 2012 (2012), Article ID 310801, 17 pages. doi:10.1155/2012/310801. https://projecteuclid.org/euclid.aaa/1364475806


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