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

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

ABSTRACT

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. "
##### Dataset: Duality for second-order symmetric multiobjective programming with cone constraints
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ABSTRACT: In this paper, a new pair of Mond-Weir type multiobjective second-order symmetric dual models with cone constraints is formulated in which the objective function is optimised with respect to an arbitrary closed convex cone. Usual duality relations are further established under K-η-bonvexity/second-order symmetric dual K-H-convexity assumptions. A nontrivial example has also been illustrated to justify the weak duality theorems. Several results including many recent works are obtained as special cases. Reference to this paper should be made as follows: Gupta, S.K. and Dangar, D. (2012) 'Duality for second-order symmetric multiobjective programming with cone constraints', Int.
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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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