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**A class of nonconvex functions and pre-variational inequalities.**
*(English)*
Zbl 0779.90067

Summary: A class of nonconvex functions is introduced, called semi-preinvex function, which includes the classes of preinvex functions and arc- connected convex functions. The Fritz-John conditions of the mathematical programming problem are derived for these kinds of functions. The pre- variational inequality is given as a necessary condition and also a sufficient condition for a mathematical programming for invex functions. The Type I function related to unconstrained problems is given as an equivalent form of the pre-variational inequality. Existence theorems for the solution of the pre-variational inequality are also proved.

### MSC:

90C26 | Nonconvex programming, global optimization |

26B25 | Convexity of real functions of several variables, generalizations |

49J40 | Variational inequalities |

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\textit{X. Q. Yang} and \textit{G.-Y. Chen}, J. Math. Anal. Appl. 169, No. 2, 359--373 (1992; Zbl 0779.90067)

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### References:

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