中文摘要：

目的给出一类极大极小半无限分式规划的最优性条件包括Kuhn-Tucker条件。方法利用Clarke-广义方向导数定义了一类新的广义一致Bρ-（p,r）-不变凸函数,并讨论了具有该广义凸性的一类极大极小半无限分式规划的最优性条件。结果在新的广义凸函数的约束下,得到了一类极大极小半无限分式规划的最优性条件。结论扩展了极大极小半无限分式规划的最优性理论。

英文摘要：

Aim To obtain the optimality conditions of min-max semi-infinite fractional programming, including Kuhn-Tueker conditions. Methods A class of a new generalized uniform Bp-（p, r）-invexity is given by using Clarke directional derivative, the optimality conditions about a class of min-max semi-infinite factional programming are studied. Results The optimality conditions about a class of min-max semi-infinite factional programming are obtained under the new generalized invexity functions. Conclusion Optimality theorem of min-max semi-infinite factional programming is improved and supplemented.