中文摘要：

提出了一类新的广义凸函数——半严格-G-E-半预不变凸函数,它是一类非常重要的广义凸函数,为半严格-G-半预不变凸函数与半严格-E-预不变凸函数的推广.首先给出例子,以说明半严格-G-E-半预不变凸函数的存在性及其与其他相关广义凸函数间的关系.然后讨论了半严格-G-E-半预不变凸函数的一些基本性质.最后,探究了半严格-G-E-半预不变凸型函数分别在无约束和有约束非线性规划问题中的重要应用,获得一系列最优性结论,并举例验证了所得结果的正确性.

英文摘要：

A new class of generalized convex functions, namely the semistrict-G-E-semiprein- vex functions were proposed, which are a class of very important generalized convex functions and make a true generalization of both the semistrict-G-semipreinvex functions and the semis- trict-E-preinvex functions. Firstly, several examples were given to illustrate the existence of semistrict-G-E-semipreinvex functions and the dependence on the related generalized convex functions. Afterwards, the basic characteristics of the semistrict-G-E-semipreinvex functions were discussed. Finally, some applications of the semistrict-G-E-semipreinvex functions in non- linear progranmting problems without constraint and with inequality constraints were studied re- spectively, and some optimality results were obtained; moreover, some examples were given to illustrate the correctness of the obtained results.