Abstract
Abstract We introduce a pair of symmetric dual problems for nondifferentiable multiobjective fractional variational problems with cone constraints over arbitrary cones. On the basis of weak efficiency, we obtain symmetric duality relations for Mond-Weir-type problems under invexity and pseudoinvexity assumptions. Our symmetric duality results extend and improve some known results in Mishra et al. (J. Math. Anal. Appl. 333:1093-1110, 2007) to the cone constraints. MSC:90C29, 90C32, 90C26.
Highlights
The notion of symmetric duality in nonlinear programming, in which the dual of the dual is the primal, was first introduced by Dorn [ ]
Suneja et al [ ] formulated a pair of Wolfe-type multiobjective symmetric dual programs over arbitrary cones, in which the objective function is optimized with respect to an arbitrary closed convex cone by assuming the functions involved to be cone-convex
We introduce a pair of symmetric duals for nondifferentiable multiobjective fractional variational problems with cone constraints over arbitrary cones
Summary
The notion of symmetric duality in nonlinear programming, in which the dual of the dual is the primal, was first introduced by Dorn [ ]. Khurana [ ] formulated a pair of Mond-Weir-type multiobjective symmetric dual programs over arbitrary cones and derived the symmetric duality theorems involving cone-pseudoinvex and strongly cone-pseudoinvex functions. Kim and Kim [ ] extended the results of Suneja et al [ ] and Khurana [ ] to nondifferentiable multiobjective symmetric dual programs for weak efficiency involving cone-invex and cone-pseudoinvex functions. Following Mond and Schechter [ ], Yang et al [ ] presented a pair of symmetric dual nonlinear fractional programming problems and established duality theorems under pseudo-convexity/pseudo-concavity assumptions on the kernel function. Ahmad et al [ ] formulated a pair of multiobjective fractional variational symmetric dual problems over cones and established duality theorems. We introduce a pair of symmetric duals for nondifferentiable multiobjective fractional variational problems with cone constraints over arbitrary cones.
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