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

• Record Type: Journal Article
• Authors: Han, Yu
• Is Part Of: Optimization. Volume 72:Number 4(2023)
• Page Start: 979
• Page End: 1008
• Publication Date: 2023-04-03
• Subjects: Vector optimization -- density theorem -- connectedness -- improvement set; 90C26 -- 90C29; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2021.2009825
• Languages: English
• ISSNs: 0233-1934

Abstract

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.