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$ V $-$ E $-invexity in $ E $-differentiable multiobjective programming

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  • In this paper, a new concept of generalized convexity is introduced for not necessarily differentiable vector optimization problems with $ E $-differentiable functions. Namely, for an $ E $-differentiable vector-valued function, the concept of $ V $-$ E $-invexity is defined as a generalization of the $ E $-differentiable $ E $-invexity notion and the concept of $ V $-invexity. Further, the sufficiency of the so-called $ E $-Karush-Kuhn-Tucker optimality conditions are established for the considered $ E $-differentiable vector optimization problems with both inequality and equality constraints under $ V $-$ E $-invexity hypotheses. Furthermore, the so-called vector $ E $-dual problem in the sense of Mond-Weir is defined for the considered $ E $-differentiable multiobjective programming problem and several $ E $-duality theorems are derived also under appropriate $ V $-$ E $-invexity assumptions.

    Mathematics Subject Classification: Primary: 90C26, 90C30, 90C46, 26B25.

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