Hybrid Algorithms for Solving Variational Inequalities, Variational Inclusions, Mixed Equilibria, and Fixed Point Problems

Abstract and Applied Analysis

Research Article

Jen-Chih Yao¹  Mu-Ming Wong³  Adrian Petrusel²  Lu-Chuan Ceng⁴ 

[1] Center for Fundamental Science, Kaohsiung Medical University, Kaohsiung 807, Taiwan, kmu.edu.tw;Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia, kau.edu.sa;Department of Applied Mathematics, Babeş-Bolyai University, 400084 Cluj-Napoca, Romania, ubbcluj.ro;Department of Applied Mathematics and Center for Theoretical Science, Chung Yuan Christian University, Chung Li 32023, Taiwan, cycu.edu.tw;Department of Mathematics, Shanghai Normal University, Shanghai 200234, China, shnu.edu.cn;Scientific Computing Key Laboratory of Shanghai Universities, Shanghai 200234, China

Others  :  1319592
DOI  :  10.1155/2014/208717

 received in 2013-11-06, accepted in 2013-12-30,  发布年份 2014

【 摘 要 】

We present a hybrid iterative algorithm for finding a common element of the set of solutions of a finite family of generalized mixed equilibrium problems, the set of solutions of a finite family of variational inequalities for inverse strong monotone mappings, the set of fixed points of an infinite family of nonexpansive mappings, and the set of solutions of a variational inclusion in a real Hilbert space. Furthermore, we prove that the proposed hybrid iterative algorithm has strong convergence under some mild conditions imposed on algorithm parameters. Here, our hybrid algorithm is based on Korpelevič’s extragradient method, hybrid steepest-descent method, and viscosity approximation method.

【 授权许可】

CC BY   
Copyright © 2014 Lu-Chuan Ceng et al. 2014

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