本文首先定义了无须可微性条件的伪-E-凸函数,它是E-凸函数和无须可微性条件的伪凸函数的真推广,举例验证了它的存在性,并讨论了它和其他函数的关系,这说明无须可微性条件的伪-E-凸函数更具一般性,应用范围更广;其次,获得了伪-E-凸函数的一些性质；最后,在最优性方面,针对伪-E-凸规划问题($\mathrm{P}$)和($\mathrm{P}_{E}$),讨论了映射E的不动点和它们的全局最优解的关系,得到了规划问题($\mathrm{P}$)的最优解的局部-全局性和全局最优解的唯一性,并分别举例验证了所得结果。
Firstly, a class of pseudo-E-convex functions without differentiability condition is defined in this paper, which is a proper generalization of E-convex functions and pseudoconvex functions without differentiability condition. The existence of such functions is verified with an example. Furthermore, the relationships between pseudo-E- convex functions and other functions are discussed. These indicate that pseudo-E-convex functions without differentiability condition are more general and have a wider range of applications. Secondly, some properties of pseudo-E-convex functions are obtained. Finally, in terms of optimality, the relationship between the fixed points of the mapping E and their global optimal solutions is discussed for the pseudo-E-convex programming problems ($\mathrm{P}$) and ($\mathrm{P}_{E}$), the local-global property of the optimal solutions and the uniqueness of the global optimal solution for programming problem ($\mathrm{P}$) are obtained, and the examples are provided to verify the results respectively.
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