| 摘要: |
| E-凸函数在优化理论中有着重要的作用.通过对比凸函数的相关性质，得到了广义E-凸函数与凸函数的关系，对文献［5］中引理的证明举出了反例，并对E-凸函数与E-单调的等价性给出了重新证明，进一步论证了在有限维空间中，f在特定的开集E(M)上任意一点都有上界；最后，针对广义E-凸函数已有的性质和结论进行了相应的推广. |
| 关键词: E-凸集 E-凸函数 拟-E-凸函数 拟-半-E-凸函数 E-单调 |
| DOI： |
| 分类号: |
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| Some New Findings of Generalized E-Convex Function |
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LI Jun1, LIU Xiao-jing2
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| Abstract: |
| The generalized E-convex function plays an important role in the optimization theory. The relationship between generalized E-convex function and convex function is obtained by comparing the correlation properties of convex functions. Then a counterexample is given for the proof of the lemma in the literature ［5］, and the equivalence between the E-convex function and the E-monotone is proved newly. It is further proved that f has an upper bound on a specific open set E(M) in a finite dimensional space. Finally, the properties and conclusions of the generalized E-convex function are generalized. |
| Key words: E-convex sets E-convex function quasi-E-convex function quasi-semi-E-convex function E-monotonicity |
