Existence and Arcwise connectedness of Robust solutions for uncertain generalized multi-objective optimization problems

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发表日期：

2025年6月20日

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M. Das,
C. Nahak,
R. N. Mohapatra

摘要

This paper investigates the existence and connectedness of robust solutions for uncertain generalized multiobjective optimization problems (UGMOPs). First, we establish the existence of robust solutions for UGMOPs by applying the scalarization method and the FAN-KKM theorem. Next, we obtain a characterization of weak and strict robust l-minimal solutions as the union of a family of scalar optimization problems. We then investigate the arcwise connectedness for both the $\preceq ^l_K$ $⪯_{K}^{l}$ -robust and $\prec ^l_K$ $≺_{K}^{l}$ -robust minimal solutions of UGMOPs by utilizing the scalarizing results and the strictly natural quasi cone convexity assumption. Necessary examples are presented to validate the results. Finally, we apply our findings to uncertain vector-valued game theory.