(F,α,ε)-凸分式半无限规划问题的ε-最优性条件

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

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.

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.