New optimality conditions and duality results of image type in differentiable mathematical programming Original Research Article

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