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Yuhao Zhang, Guolin Yu, Wenyan Han, Directional derivative of set-valued mappings involving generalized oriented distance functions and applications to set optimization

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DOI: 10.23952/asvao.8.2026.2.07
Volume 8, Issue 2, 1 August 2026, Pages 239-252

 

Abstract. This paper focuses on the directional derivative and subdifferential of set-valued mappings via nonlinear scalarizing functions. Firstly, we define the directional derivative and subdifferential of set-valued mappings by using a generalized oriented distance function. Secondly, we systematically investigated the operational rules, positive homogeneity, chain rule, and upper semicontinuity of the directional derivative for set-valued mappings. Thirdly, we examine the convexity and weak* closedness of the subdifferential of set-valued mappings, as well as its relationship with the directional derivative. Finally, the optimality conditions for set optimization problems are established by utilizing the introduced subdifferential.

 

How to Cite this Article:
Y. Zhang, G. Yu, W. Han, Directional derivative of set-valued mappings involving generalized oriented distance functions and applications to set optimization, Appl. Set-Valued Anal. Optim. 8 (2026), 239-252.