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G-pre-invex functions in mathematical programming. (English) Zbl 1219.90126
Summary: We introduce the concept of G-pre-invex functions with respect to η defined on an invex set with respect to η. These function unify the concepts of nondifferentiable convexity, pre-invexity and r-pre-invexity. Furthermore, relationships of G-pre-invex functions to various introduced earlier pre-invexity concepts are also discussed. Some (geometric) properties of this class of functions are also derived. Finally, optimality results are established for optimization problems under appropriate G-pre-invexity conditions.
MSC:
90C26Nonconvex programming, global optimization
26B25Convexity and generalizations (several real variables)
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