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 \(\eta\) .


90C46 Optimality conditions and duality in mathematical programming
90C26 Nonconvex programming, global optimization
26B25 Convexity of real functions of several variables, generalizations
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