中文摘要：

首先在给出α-预不变凸函数和强α-预不变凸函数的基础上,讨论了二者之间的关系,得到了强α-预不变凸函数的几个性质,其次讨论了强α-预不变凸函数分别在无约束和带不等式约束的非线性规划问题中的应用。这些结果在一定程度上完善了对强α-预不变凸函数的研究。

英文摘要：

Based on giving α-preinex function and strong α-preinex function, this paper explores the relationship between them, and gets some properties of strong α-preinex function, then discusses the application of strong α-preinex function in nonlinear programming problems without constraint and with inequality constraint. These results have improved the research on strong α-preinex functions to some extent.