Connectedness of solution sets in set optimization with Minkowski order
Optimization Eruditorum, Volume 3, Issue 2, August 2026, Pages 75–85
HAN YANG
Chongqing Jiaotong University, Chongqing 400074, P.R. China
XIN YANG
Chongqing Jiaotong University, Chongqing 400074, P.R. China
ELISABETH Köbis
Norwegian University of Science and Technology, Trondheim 7491, Norway
Zai Yun Peng
Yunnan Normal University, Kunming 650092, P.R. China
Chongqing Jiaotong University, Chongqing 400074, P.R. China
Abstract
This paper investigates set optimization problems under the Minkowski order relation, focusing on the connectedness of approximate solution sets via a scalarization approach. First, by employing the Gerstewitz function and assuming the set-valued mapping is continuous with compact values, the continuity of this function is established. Subsequently, the convexity and semicontinuity of the associated mapping are analyzed. Furthermore, the connectedness of the weak approximate solution set is proved. The obtained results enrich the scalarization theory in set optimization and provide a theoretical foundation for subsequent research on the stability of solution sets.
Cite this Article as
Han. Yang, Xin. Yang, Elisabeth Köbis, and Zai Yun Peng, Connectedness of solution sets in set optimization with Minkowski order, Optimization Eruditorum, 3(2), 75–85, 2026