Abstract
In this paper, Mond-Weir and Wolfe type duals for multiobjective variational control problems are formulated. Several duality theorems are established relating efficient solutions of the primal and dual multiobjective variational control problems under $$(\Phi , \rho )$$ ( ? , ? ) -invexity. The results generalize a number of duality results previously established for multiobjective variational control problems under other generalized convexity assumptions.
Highlights
Duality constitute an essential part of study of mathematical programming in the sense that these lay down the foundation of algorithms for a solution of an optimization problem
Duality theory for multiobjective variational problems has been of much interest, and several contributions have been made to its development
By utilizing this concept of generalized convexity, we prove Mond Weir type and Wolfe type duality results for multiobjective variational control programming problem involving (, ρ)invex functions with respect to, not necessarily, the same ρ
Summary
Duality constitute an essential part of study of mathematical programming in the sense that these lay down the foundation of algorithms for a solution of an optimization problem. The notion of scalar ( , ρ)-invexity is extended to the continuous case and it is defined for multiobjective variational control problems By utilizing this concept of generalized convexity, we prove Mond Weir type and Wolfe type duality results for multiobjective variational control programming problem involving ( , ρ)invex functions with respect to, not necessarily, the same ρ (with the exception of those the equality constraints for which the associated piecewise smooth functions satisfying the constraints of duals are negative). The duality results established in this paper under ( , ρ)-invexity are true for such nonconvex multiobjective variational control problems as problem (MVPP1) considered in Example 5 for which most of the generalized convexity notions may avoid
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