Geodesic
Sufficient Optimality Conditions and Duality for Nonsmooth Multiobjective Optimization Problems Via Higher Order Strong Convexity
Yugoslav journal of operations research, Tome 27 (2017) no. 2, p. 227 .

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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.
Classification : 90C29, 90C46, 49N15
Keywords: Nonsmooth Multiobjective Programming, Support Functions, Strict Minimizers, Optimality Conditions, Mixed Duality 
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     author = {Balendu B. Upadhyay and Ningthoujam Priyobarta and Yumnam S. Rohen},
     title = {Sufficient {Optimality} {Conditions} and {Duality} for {Nonsmooth} {Multiobjective} {Optimization} {Problems} {Via} {Higher} {Order} {Strong} {Convexity}},
     journal = {Yugoslav journal of operations research},
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Balendu B. Upadhyay; Ningthoujam Priyobarta; Yumnam S. Rohen. Sufficient Optimality Conditions and Duality for Nonsmooth Multiobjective Optimization Problems Via Higher Order Strong Convexity. Yugoslav journal of operations research, Tome 27 (2017) no. 2, p. 227 . http://geodesic.mathdoc.fr/item/YJOR_2017_27_2_a5/