Abstract
Based on the improvement set E, this paper aims at investigating density and connectedness of the sets of E-optimal points, weak E-optimal points, E-quasi-optimal points, E-Benson proper optimal points, E-super optimal points and E-strictly optimal points. By virtue of the separation theorem for convex sets, we obtain the scalarizaiton results for the sets of E-optimal points, weak E-optimal points, E-Benson proper optimal points, E-super optimal points and E-strictly optimal points. Then we make a new attempt to establish some density theorems for the sets of these optimal points. Finally, we investigate connectedness and arcwise connectedness of the sets of various notions of E-optimality by using the scalarization method and the density theorems.
Acknowledgments
The author is grateful to the editor and the two anonymous reviewers for their valuable comments and suggestions.
Disclosure statement
No potential conflict of interest was reported by the author(s).