中文摘要：

文章在弧连通集S真包含R^n上的实值函数f：S→R是弧连通函数的定义下，给出相关的广义弧连通函数定义。这类函数是凸性的推广，它们满足确定的局部一全局极值性。反过来，在某些条件下，满足局部-全局极值性的函数必是这些广义函数类之一。在广义弧连通的假设下建立了约束规划（ACP）minx∈Sf（x），s.t.g（x）≤0的最优性充分条件。

英文摘要：

The paper defines general arcwise connected function（ACF） by the definition of arcwise connected function f： S → R on an arcwise connected set S lohtain in R^n. This kind of function is the generalization of convex function which satisfies the local or global optimality. On the other hand, under some conditions the function with this property must be one of general functions. Furthermore, the optimalilty conditions of the constraint program （ACP） min x∈S f（x）, s.t. g（x）≤ 0 are considered under the assumption of general arcwise connected.