Abstract
Under ρ − (η, θ)‐invexity assumptions on the functions involved, weak, strong, and converse duality theorems are proved to relate properly efficient solutions of the primal and dual problems for a multiobjective programming problem.
Highlights
The notion of η-invexity was originally introduced by Hanson [6] who showed that, for a nonlinear programming problem whose objective and constrained functions are η-invex, the Karush-Kuhn-Tucker necessary optimality conditions are sufficient
Introducing the concept of proper efficiency of solutions, Geoffrion [5] proved an equivalence between multiobjective program with convex functions and a related parametric objective program
Weir [9] formulated a dual program for a multiobjective program having differentiable convex functions
Summary
The notion of η-invexity was originally introduced by Hanson [6] who showed that, for a nonlinear programming problem whose objective and constrained functions are η-invex (all with respect to the same η), the Karush-Kuhn-Tucker necessary optimality conditions are sufficient. Introducing the concept of proper efficiency of solutions, Geoffrion [5] proved an equivalence between multiobjective program with convex functions and a related parametric (scalar) objective program. Using this equivalence, Weir [9] formulated a dual program for a multiobjective program having differentiable convex functions. Das and Nanda [3] have studied the duality theorems of Mond-Weir type for a multiobjective programming problem with semilocally invex functions. Duality results (weak, strong, and converse duality theorems) are proved for multiobjective programming problem under ρ − (η,θ)-invexity assumptions on the functions involved.
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