Arcwise connectedness of solution sets in set optimization via set less order
Applicable Nonlinear Analysis, Volume 2, Issue 2, August 2025, Pages: 81–90
XIN YANG
Chongqing Jiaotong University, Chongqing 400074, P.R. China
ZAI YUN PENG
Chongqing Jiaotong University, Chongqing 400074, P.R. China
LAM QUOC ANH
Teacher College, Cantho University, Cantho 94000, Vietnam
MINH N. DAO
School of Science, RMIT University, Melbourne 3010, Australia
Abstract
This paper investigates the arcwise connectedness of approximate solution sets for set optimization problems under the set less order relation via a scalarization approach. First, we establish the continuity of a novel nonlinear scalarization function constructed based on the set less criterion. Next, scalarization properties of the approximate solution sets are rigorously derived. Finally, we derive arcwise connectedness of weak approximate solutions for set optimization problems. These results enrich the exploration of scalarization and connectedness under set less order relations and provide a theoretical foundation for subsequent research.
Cite this Article as
Xin Yang, Zai Yun Peng, Lam Quoc Anh, and Minh N. Dao, Arcwise connectedness of solution sets in set optimization via set less order, Applicable Nonlinear Analysis, 2(2), 81–90, 2025