（F，α，ε）-凸分式半无限规划问题的ε-最优性条件

首次引入了（F，α，ε）-凸函数、（F，α，ε）-拟凸函数和（F，α，ε）-伪凸函数等概念，对已有的凸函数进行了推广，并研究了涉及这类函数的一类分式半无限规划的ε-最优性条件，得到了一些有意义的结果．这些结果不仅是现有某些结果的推广，而且为诸如资源分配问题、投资组合等问题的研究提供了依据，也为理论上研究分式规划提供了参考．

ε-Optimality conditions for a class of fractional semi-infinite programming with (F,α,ε)-convex functions

In this paper, some classes of （F,α,ε）-convex function, （F,α,ε）-quasi function and （F,α,ε）-pseudo function are defined. Based on the above, a class of fractional semi-infinite programming are considered, which is generalization of the old convex functions . Then, a class of fractional semi-infinite programming invoking these generalized convex functions are studied, some interesting ε-optimality conditions are obtained. The results obtained not only generalize some of the present researches, but are a kind of basis for salving the questions in resource allocation and portfolio selection etc, they are also theoretical references for the study of fractional programming.