Abstract
In this paper, a pair of nondifferentiable multiobjective fractional programming problems is formulated. For a differentiable function, we introduce the definition of higher-order (F, α, ρ, d)-convexity, which extends some kinds of generalized convexity, such as second order F-convexity and higher-order F -convexity. Under the higher-order (F, α, ρ, d)-convexity assumptions, we prove the higher-order weak, higher-order strong and higher-order converse duality theorems.Mathematics Subject Classification (2010) 90C29; 90C30; 90C46.
Highlights
Symmetric duality in nonlinear programming in which the dual of the dual is the primal was introduced by Dorn [1]
Mond and Weir [4] gave another pair of symmetric dual nonlinear programs in which a weaker convexity assumption was imposed on involved functions
Yang et al [10] discussed a class of nondifferentiable multiobjective fractional programming problems, and proved duality theorems under the assumptions of invex functions
Summary
Symmetric duality in nonlinear programming in which the dual of the dual is the primal was introduced by Dorn [1]. Mond [3] presented a slightly different pair of symmetric dual nonlinear programs and obtained more generalized duality results than that of Dantzig et al [2]. Mond and Weir [4] gave another pair of symmetric dual nonlinear programs in which a weaker convexity assumption was imposed on involved functions. Pandey [9] introduced second-order h-invex function for multiobjective fractional programming problem and established weak and strong duality theorems. Yang et al [10] discussed a class of nondifferentiable multiobjective fractional programming problems, and proved duality theorems under the assumptions of invex (pseudoinvex, pseudoincave) functions. Mangasarian [11] formulated a class of higher-order dual problems for the nonlinear programming problem by introducing twice differentiable functions.
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