Zai-Yun Peng, Xue-Jing Chen, Jen-Chih Yao, Ka Fai Cedric Yiu, Yun-Bin Zhao, On the stability for parametric set optimization problems via improvement sets without the strict convexity
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DOI: 10.23952/jnva.9.2025.5.01
Volume 9, Issue 5, 1 October 2025, Pages 637-654
Abstract. In this paper, we aim to discuss the stability of parametric set optimization problems via improvement sets. First, we establish some convergence results for set-valued mappings. Next, under new assumptions, the Berge upper and lower semicontinuity of upper level mappings for parametric set optimization problems with the upper relation are investigated. Then, under suitable assumptions, the sufficient conditions for Berge upper and lower semicontinuity of (weak) minimal solution mappings for parametric set optimization problems via improvement sets are established.
How to Cite this Article:
Z.Y. Peng, X.J. Chen, J.C. Yao, K.F.C. Yiu, Y.B. Zhao, On the stability for parametric set optimization problems via improvement sets without the strict convexity, J. Nonlinear Var. Anal. 9 (2025), 637-654.