\(G\)-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.


90C26 Nonconvex programming, global optimization
26B25 Convexity of real functions of several variables, generalizations
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