Abstract
In this paper, we introduce a new class of generalized dI-univexity in which each component of the objective and constraint functions is directionally differentiable in its own direction di for a nondifferentiable multiobjective programming problem. Based upon these generalized functions, sufficient optimality conditions are established for a feasible point to be efficient and properly efficient under the generalised dI-univexity requirements. Moreover, weak, strong and strict converse duality theorems are also derived for Mond-Weir type dual programs.
Highlights
The field of multiobjective programming, known as vector programming, has grown remarkably in different directions in the setting of optimality conditions and duality theory
Agarwal et al [21] introduced a new class of generalized d, type I for a non-smooth multiobjective programming problem and discussed optimality conditions and duality results
We introduce dI V -univexity and generalized dI V -univexity in which each component of the objective and constraint functions of a multiobjective programming problem is semidirectionally differentiable in its own direction di
Summary
The field of multiobjective programming, known as vector programming, has grown remarkably in different directions in the setting of optimality conditions and duality theory. Kaul et al [8] extended the concept of type I and its generalizations for a multiobjective programming problem They investigated optimality conditions and derived Wolfe type and Mond-Weir type duality results. The duality results for a Mond-Weir type dual are derived in [20] They observed that the Karush-Kuhn-Tucker sufficient conditions discussed in [16,17,18] are not applicable. Agarwal et al [21] introduced a new class of generalized d , type I for a non-smooth multiobjective programming problem and discussed optimality conditions and duality results. Various Karush-Kuhn-Tucker sufficient optimality conditions for efficient and properly efficient solutions to the problem are established involving new classes of semidirectionally differentiable generalized type I functions. The results in this paper extend many earlier work appeared in the literature [9,10,12,14,15,16, 19]
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