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Second-order optimality conditions in nonsmooth vector optimization

Yadav Priyanka

Control and Cybernetics

2023

Vol. 52, No. 1

35--51

In this paper, we introduce new classes of nonsmooth second-order cone-convex functions and respective generalizations in terms of first and second-order directional derivative. These classes encapsulate several already existing classes of cone-convex functions and their weaker variants. Second-order KKT type sufficient optimality conditions and duality results for a nonsmooth vector optimization problem are proved using these functions. The results have been supported by examples.