On vector optimization problems and vector variational inequalities using convexificators

Abstract

In this paper, we establish some results which exhibit an application of convexificators in vector optimization problems (VOPs) and vector variational inequaities involving locally Lipschitz functions. We formulate vector variational inequalities of Stampacchia and Minty type in terms of convexificators and use these vector variational inequalities as a tool to find out necessary and sufficient conditions for a point to be a vector minimal point of the VOP. We also consider the corresponding weak versions of the vector variational inequalities and establish several results to find out weak vector minimal points.

Keywords:

• Vector variational inequalities
• vector optimization problems
• vector minimal points
• weak vector minimal points
• convexificators
• convexity
• monotonicity

Acknowledgements

The authors are thankful to the anonymous referees for their valuable comments and suggestions which helped to improve the presentation of the paper.

Notes

No potential conflict of interest was reported by the authors.