Abstract
In this paper, a new class of higher order (ϕ, ρ)-invex function is introduced with an example, in which the sublinearity and convexity assumption on ϕ with respect to third argument is relaxed. A pair of higher order Wolfe type multiobjective symmetric dual for a class of nondifferentiable multiobjective programming involving square root term is presented and the weak duality, strong duality and converse duality theorems are established with their proofs under higher order (ϕ, ρ)-invexity and (ϕ, ρ)-incavity assumption. Self duality theorem is proved for the proposed dual program. These results are used to discuss Wolfe type higher-order symmetric minimax mixed integer dual problems. A numerical example is developed where the results of weak and strong duality theorems can be applied. Discussion on some particular cases shows that our results generalize earlier results in related domain.
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Tripathy, A.K., Devi, G. Wolfe Type Higher Order Multiple Objective Nondifferentiable Symmetric Dual Programming with Generalized Invex Function. J Math Model Algor 13, 557–577 (2014). https://doi.org/10.1007/s10852-013-9247-3
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DOI: https://doi.org/10.1007/s10852-013-9247-3