A general iterative algorithm for vector equilibrium problem

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, 52 (2003), 301–316], [S.-H. Wang, Q.-Y. Li, Optimization, 64 (2015), 2049–2063], and [B. Cheng, S.-Y. Liu, J. Lanzhou Univ. Nat. Sci., 45 (2009), 105–109].