Abstract
We study a nonlinear multiple objective fractional programming with inequality constraints where each component of functions occurring in the problem is considered semidifferentiable along its own direction instead of the same direction. New Fritz John type necessary and Karush-Kuhn-Tucker type necessary and sufficient efficiency conditions are obtained for a feasible point to be weakly efficient or efficient. Furthermore, a general Mond-Weir dual is formulated and weak and strong duality results are proved using concepts of generalized semilocally V-type I-preinvex functions. This contribution extends earlier results of Preda (2003), Mishra et al. (2005), Niculescu (2007), and Mishra and Rautela (2009), and generalizes results obtained in the literature on this topic.
Highlights
Because of many practical optimization problems where the objective functions are quotients of two functions, multiobjective fractional programming has received much interest and has grown significantly in different directions in the setting of efficiency conditions and duality theory these later years
New Fritz John type necessary and Karush-Kuhn-Tucker type necessary and sufficient efficiency conditions are obtained for a feasible point to be weakly efficient or efficient
Efficiency conditions and duality models for multiobjective fractional subset programming problems are studied by Preda et al [9], Verma [10], and Zalmai [11,12,13]
Summary
Because of many practical optimization problems where the objective functions are quotients of two functions, multiobjective fractional programming has received much interest and has grown significantly in different directions in the setting of efficiency conditions and duality theory these later years. In Preda [7], necessary and sufficient efficiency conditions for a nonlinear fractional multiple objective programming problem are obtained involving η-semidifferentiable functions. By considering the invexity with respect to different (ηi)i (each function occurring in the studied problem is considered with respect to its own function ηi instead of the same function η), Slimani and Radjef [32,33,34] have obtained necessary and sufficient optimality/efficiency conditions and duality results for nonlinear scalar and (nondifferentiable) multiobjective problems. We extend the works of Mishra and Rautela [4], Mishra et al [5], Niculescu [6], and Preda [7] and generalize results obtained in the literature on this topic
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