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

In this paper, a new class of differentiable functions, called G-invex functions with respect to 71, 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 eta. (c) 2006 Elsevier Ltd. All rights reserved.