Density and connectedness of optimal points with respect to improvement sets. (3rd April 2023) - Han, Yu
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.