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In this paper, we define some new generalizations of strongly convex   functions of order m for locally Lipschitz functions using Clarke   subdifferential. Suitable examples illustrating the non emptiness of the   newly defined classes of functions and their relationships with classical   notions of pseudoconvexity and quasiconvexity are provided. These   generalizations are then employed to establish sufficient optimality   conditions for a nonsmooth multiobjective optimization problem involving   support functions of compact convex sets. Furthermore, we formulate a mixed   type dual model for the primal problem and establish weak and strong duality   theorems using the notion of strict efficiency of order m. The results   presented in this paper extend and unify several known results from the   literature to a more general class of functions as well as optimization   problems

Sufficient optimality conditions and duality for nonsmooth multiobjective optimization problems via higher order strong convexity