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New optimality conditions and duality results of $G$ type in differentiable mathematical programming. (English) Zbl 1143.90034
Summary: A new class of differentiable functions, called $G$-invex functions with respect to $\eta$ , 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 $\eta$ .
##### MSC:
 90C46 Optimality conditions, duality 90C26 Nonconvex programming, global optimization 26B25 Convexity and generalizations (several real variables)