New optimality conditions and duality results of G type in differentiable mathematical programming

Abstract In this paper, a new class of differentiable functions, called G -invex functions with respect to η , is introduced by extending the definition of invex functions. New necessary optimality conditions of G -F. John and G -Karush–Kuhn–Tucker type are obtained for differentiable constrained mathematical programming problems. The G -invexity concept introduced is used to prove the sufficiency of these necessary optimality conditions. Further, a so-called G -Mond–Weir-type dual is formulated and various duality results are also established by assuming the functions involved to be G -invex with respect to the same function η .

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