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Volume 5, Issue 6, 1 December 2021, Pages 909-927
Abstract. In this paper, based on the oriented distance function of Hiriart-Urruty, we investigate a set scalarization function of sup-inf type. Some properties of the set scalarization function allow us to define the Dini directional derivatives for set-valued mappings, which is an extension of the classical Dini derivatives for scalar functions. We also obtain some properties of the Dini directional derivatives for set-valued mappings. As applications, we derive some necessary and sufficient optimality conditions for set optimization problems.
How to Cite this Article:
Yu Han, Nan-Jing Huang, Ching-Feng Wen, A set scalarization function and Dini directional derivatives with applications in set optimization problems, J. Nonlinear Var. Anal. 5 (2021), 909-927.