Multiobjective higher-order symmetric duality involving generalized cone-invex functions

Department of Applied Mathematics, Birla Institute of Technology Mesra, Ranchi-835 215, India
Computers & Mathematics with Applications (Impact Factor: 1.7). 12/2010; 60(12):3187-3192. DOI: 10.1016/j.camwa.2010.10.023
Source: DBLP


In this paper, a pair of Mond–Weir type multiobjective higher-order symmetric dual programs over arbitrary cones is formulated and usual duality results are established under higher-order K-preinvexity/K-pseudoinvexity assumptions. Symmetric minimax mixed integer primal and dual problems are also discussed.

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    • "Ahmad et al. (2011) presented a second-order dual for a nondifferentiable fractional programming problem which consists of maximising the ratio of functions involving square root terms of positive semidefinite quadratic forms and established duality results using second-order (F, α, ρ, d)-convexity assumptions. Gupta and Jayswal (2010) gave a Mond-Weir type higher-order multiobjective symmetric dual programs over arbitrary cones and proved duality results under higher-order cone-invexity/pseudoinvexity assumptions. Preda et al. (2011) established duality results for a fractional programming problem by replacing convexity/sublinearity assumptions on F by quasiconvexity. "
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    ABSTRACT: In this paper we establish weak, strong and converse duality results for a pair of Wolfe type higher-order symmetric dual problems over cones under the assumption of higher-order cone-invexity. We also introduce the concepts of higher-order strictly and strongly cone-pseudoinvexity and use them to obtain weak, strong and converse duality results for the pair of Mond-Weir type higher-order symmetric dual problems.
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    ABSTRACT: In this paper, a pair of Wolfe type higher-order nondifferentiable symmetric dual programs over arbitrary cones has been studied and then well-suited duality relations have been established considering K-F convexity assumptions. An example which satisfies the weak duality relation has also been depicted. MSC: 90C29, 90C30, 49N15.
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