广义凸函数的上图与水平集

发布时间：2018-04-17 04:06

本文选题：广义凸函数 + 广义凸结构　；参考：《重庆师范大学学报(自然科学版)》2017年01期

【摘要】：【目的】对于广义凸集与广义凸函数的研究是十分基础而重要的课题,只有广义凸性的基础理论研究不断完善,对广义凸规划的全面深入的研究才会成为可能。【方法】受凸函数的一个基本结果启发,给出概念并借助相关结果开展论证。【结果】简化了已有文献所给出的广义凸函数概念,指出函数的广义凸性与函数上图的广义凸性之间的等价关系,并给出下半连续前提下,F-G广义凸函数与F-G广义弱凸函数之间等价性的新证明。最后,指出函数的广义凸性与函数水平集的广义凸性之间的内在联系。【结论】将广义凸集和广义凸函数统一在一个结构框架下进行研究,建立了二者之间的桥梁纽带。
[Abstract]:[objective] for the study of generalized convex sets and generalized convex functions is a very basic and important subject, only the basic theory of generalized convexity is continuously improved.It is possible to study the generalized convex programming thoroughly. [method] is inspired by a basic result of convex function.The concept of generalized convex function is simplified and the equivalent relation between the generalized convexity of function and the generalized convexity of function is pointed out.A new proof of the equivalence between F-G generalized convex function and F-G generalized weak convex function under the condition of lower semicontinuous is given.Finally, the inherent relationship between the generalized convexity of functions and the generalized convexity of level sets of functions is pointed out. [conclusion] the generalized convex sets and generalized convex functions are studied under a single structure frame, and the bridge ties between them are established.
【作者单位】：佳木斯大学理学院数学系;广西大学数学与信息学院;
【基金】：黑龙江省教育厅科学技术研究项目(No.12531684)
【分类号】：O174.13

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