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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 $\eta$ defined on an invex set with respect to $\eta$. 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:
 90C26 Nonconvex programming, global optimization 26B25 Convexity and generalizations (several real variables)
##### References:
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