An iterative method for solving the strong vector equilibrium problem with variable domination structure

Abstract

In this paper, an iterative algorithm for solving the strong vector equilibrium problem with variable domination structure (VSVEP) is considered. First, an auxiliary problem for the VSVEP is introduced and the relationships between the auxiliary problem and VSVEP are discussed. Then, using the auxiliary principle technique, a projection iterative algorithm to compute the approximate solutions of the VSVEP is proposed and analysed. Furthermore, convergence of the iterative sequences generated by this algorithm is investigated under suitable conditions of continuity and convexity. These results extend and improve some recent works in this field.

Keywords:

• Strong vector equilibrium problem
• variable domination structure
• auxiliary problem
• projection iterative method
• cosmically upper continuity

AMS Subject Classifications:

• 65K15
• 47J25
• 90C33

Acknowledgements

The authors are grateful to the editor and referees for valuable comments and suggestions to improve the previous draft and help form the present version of this paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant number 11661055], [grant number 11201216], [grant number 11661056], [grant number 11771198]; the Natural Science Foundation of Jiangxi Province [grant number 20151BAB201020]; the China Postdoctoral Science Foundation [grant number 2015M582047]; the Postdoctoral Science Foundation of Jiangxi Province [grant number 2016KY58]; the Science Fund of the Education Department of Jiangxi Province [grant number GJJ160063].