Well-posedness and stability in vector optimization problems using Henig proper efficiency

Abstract

In this article, we study well-posedness and stability aspects for vector optimization in terms of minimizing sequences defined using the notion of Henig proper efficiency. We justify the importance of set convergence in the study of well-posedness of vector problems by establishing characterization of well-posedness in terms of upper Hausdorff convergence of a minimizing sequence of sets to the set of Henig proper efficient solutions. Under certain compactness assumptions, a convex vector optimization problem is shown to be well-posed. Finally, the stability of vector optimization is discussed by considering a perturbed problem with the objective function being continuous. By assuming the upper semicontinuity of certain set-valued maps associated with the perturbed problem, we establish the upper semicontinuity of the solution map.

Keywords:

• vector optimization
• Henig proper efficiency
• well-posedness
• Hausdorff convergence
• upper semicontinuity

AMS Subject Classifications::

• 90C29
• 90C31
• 49K40

Acknowledgements

The authors are grateful to the referees for their valuable comments and suggestions. Research of C.S. Lalitha is supported by R&D Doctoral Research programme for University faculty.