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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 and duality in mathematical programming |

90C26 | Nonconvex programming, global optimization |

26B25 | Convexity of real functions of several variables, generalizations |

### Keywords:

\(G\)-invex function with respect to \(\eta\); \(G\)-F. John necessary optimality conditions; \(G\)-Karush-Kuhn-Tucker optimality conditions; \(G\)-type constraint qualification; duality
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\textit{T. Antczak}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 66, No. 7, 1617--1632 (2007; Zbl 1143.90034)

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### References:

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