半严格-G-半预不变凸性与最优化

提出了一类新的广义凸函数——半严格-G-半预不变凸函数，它是一类重要的广义凸函数，是半严格预不变凸函数和半严格-G-预不变凸函数的真推广．首先，用例子说明了半严格-G-半预不变凸函数的存在性，并给出例子说明它是与G-半预不变凸函数不同的一类函数；然后，给出了半严格-G-半预不变凸函数的几个基本性质；最后，讨论了半严格-G-半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，得到了一些最优性结果，并举例验证所得结论的正确性．

Semistrict-G-Semi-preinvexity and Optimization

A class of new generalized convex function——semistrict-G-semi-preinvex functions is given.It is an important class of generalized convex function. It is a true generalization of semistrict preinvex functions and semistrict-G-preinvex functions. First, an example was given to show that there exist semistrict-G-semi-preinvex functions. At the same time, examples were given to show that the semistrict-G-semi-preinvex functions were different from G-semi-preinvex functions. Then, some properties of the semistrict-G-semi-preinvex functions were discussed. Finally, some optimality results were obtained in nonlinear programming problems without constraint and with inequality constraint, and examples were given for illustration of the corresponding results.