Nondifferentiable multiobjective programming under generalized -invexity

Efficiency and Duality in Nondifferentiable Multiobjective Programming Involving Directional Derivative

“…x f x Following Jeyakumar and Mond [24], Kaul et al [8] and Slimani and Radjef [20], we give the following definitions. , : , :…”

“…Recently, Silmani and Radjef [20] introduced generalzed d I -invexity in which each component of the objective and constraint functions is directionally differentiable in its own direction and established the necessary and sufficient conditions for efficient and properly efficient solutions. The duality results for a Mond-Weir type dual are also derived in [20]. They also observed that the Karush-Kuhn-Tucker sufficient conditions discussed in [16][17][18] …”

Sufficiency and Duality in Nonsmooth Multiobjective Programming Problem under Generalized Univex Functions

“…Definition 7 (Slimani and Radjef [12]). The function ℎ is said to be semidirectionally differentiable at ∈ in the direction ( , ) if its directional derivative ℎ ( ; ( , )) exists finite for all ∈ .…”

“…In this paper, we introduce a new generalized class of ( , , , )--V-type I univex functions which generalizes the class of functions introduced by Kharbanda et al [18], Ahmad [17], Slimani and Radjef [12], Mishra and Noor [10], Mishra et al [16], Antczak [9], Suneja and Srivastava [19], and Ye [8]. Further, we establish weak, strong, converse, and strict converse duality results for Mond-Weir type multiobjective dual program.…”

“…Nahak and Mohapatra [11] obtained duality results for multiobjective programming problem under ( ---) invexity assumptions. Slimani and Radjef [12] introduced a far wider class of nondifferentiable functions called -V-type I functions in which each component is directionally differentiable in its own direction instead of the same direction and established sufficient optimality and duality results.…”