强预不变凸函数的新性质及应用

New Characteristics and Application of Strictly Pre-invex Functions

对一类新的广义凸函数-强预不变凸函数作了进一步研究。首先给出例子说明了此类广义凸函数的存在性,然后利用强η-不变凸集和函数的上图(E(f)={(x,α):x∈K,α∈R,f(x)≤α})得到了强预不变凸函数的几个重要性质,并用另一方法给出它的一个判别定理的简化证明,最后还给出了强预不变凸函数在数学规划问题中的一个重要应用,从而完善了对此类广义凸函数的研究。

A new class of important generalized convex functions -- prequasi-invex function is further discussed. To improve research on the generalized convex function, some new characteristics of the prequasi-invex function are figured out by means of the cographical set of function （E（f）={（x,α）：x∈K,α∈f（x）≤α}） and -invex set, and its two applications in the mathematical programming problem are proposed. So the study of this type generalized convex function becomes further now.