## 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
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### References:

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