Vector equilibrium problems under improvement sets and linear scalarization with stability applications

Abstract

In this paper, for vector equilibrium problems where the ordering relations are defined via improvement sets, linear scalarization characterizations are established, which include the well-known ones for vector optimization problems in the literature as special cases. By applying the obtained results, some continuity (both lower and upper semicontinuities) conclusions of parametric problems with respect to vector equilibria through improvement sets are deduced using scalarization approaches. Several unsolved or interesting problems are also proposed.

Keywords:

• improvement set
• scalarization
• vector equilibrium problems
• semicontinuity
• strict pseudomonotonicity

Mathematics Subject Classification 2010:

• 49K40
• 90C31
• 47J20

Disclosure statement

No potential conflict of interest was reported by the authors.

Acknowledgments

The authors gratefully thank the anonymous referees and the associate editor for their constructive suggestions and comments, which helped to improve the paper. Also thanks to Hongzhi Wei (Chongqing University) for helpful discussions on improvement sets.

Additional information

Funding

This research was supported by the National Natural Science Foundation of China (Grant numbers: 11301567, 11171362 and 11571055) and the Fundamental Research Funds for the Central Universities (Grant number: 106112015CDJXY100002).