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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 of real functions of several variables, generalizations |

### Keywords:

\(G\)-pre-invex function with respect to \(\eta \); invex set with respect to \(\eta\); \(G\)-invex set with respect to \(\eta \); optimality
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\textit{T. Antczak}, J. Comput. Appl. Math. 217, No. 1, 212--226 (2008; Zbl 1219.90126)

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### References:

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