A general iterative algorithm for vector equilibrium problem

Volume 10, Issue 8, pp 4337--4351 http://dx.doi.org/10.22436/jnsa.010.08.27

Publication Date: August 24, 2017 Submission Date: April 29, 2017

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Authors

Jin-xia Huang - Department of Mathematics, Nanchang University, Nanchang, Jiangxi 330031, China. San-hua Wang - Department of Mathematics, Nanchang University, Nanchang, Jiangxi 330031, China. - Post-doctor Station of Management Science and Engineering, Nanchang University, Jiangxi 330031, China. Jia-yu Mao - Department of Mathematics, Nanchang University, Nanchang, Jiangxi 330031, China.

Abstract

In this paper, iterative algorithm for strong vector equilibrium problem (SVEP) is studied. Firstly, an auxiliary problem for SVEP is introduced and the relationships between the auxiliary problem and SVEP are discussed. Then, based on the auxiliary problem, a general iterative algorithm for SVEP is proposed. Moreover, analysis of convergence of this general iterative algorithm is investigated under suitable conditions of cone-continuity and cone-convexity. The main results obtained in this paper extend and develop the corresponding ones of [A. N. Iusem, W. Sosa, Optimization, \(\bf 52\) (2003), 301--316], [S.-H. Wang, Q.-Y. Li, Optimization, \(\bf 64\) (2015), 2049--2063], and [B. Cheng, S.-Y. Liu, J. Lanzhou Univ. Nat. Sci., \(\bf 45\) (2009), 105--109].

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Keywords

• Vector equilibrium problem
• auxiliary problem
• iterative algorithm
• metric projection
• cone-continuity.

MSC

•  49J27
•  49J40

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