广义凸函数的结构理论

发布时间：2018-05-28 18:12

本文选题：F-G广义凸函数 + F凸函数　；参考：《重庆师范大学学报(自然科学版)》2017年02期

【摘要】：【目的】对广义凸函数的性质研究,特别是建立可微前提下广义凸函数与其梯度相关的等价刻画,为函数广义凸性的判别及它在规划方面的应用提供理论依据。【方法】利用已有相关结果,通过建立广义凸函数与一元凸(拟凸)函数的等价关系,进而将凸(拟凸)函数的性质移植给广义凸函数。【结果】指出了F凸(拟凸)函数与凸(拟凸)函数之间的等价关系,进而给出可微F凸(拟凸)函数的与梯度相关的等价刻画。最后,作为应用,利用所得结果给出GA-凸函数的若干判别方法。【结论】将凸分析的若干基本结果在广义凸函数方面做了统一推广,解决了可微F凸(拟凸)函数的判别问题。
[Abstract]:[objective] to study the properties of generalized convex functions, especially to establish the equivalent characterizations of the correlation between generalized convex functions and their gradients under differentiable premises. This paper provides a theoretical basis for the discrimination of generalized convexity of function and its application in programming. [methods] by using the existing results, the equivalent relation between generalized convex function and univariate convex (quasiconvex) function is established. Then the properties of convex (quasiconvex) functions are transplanted to generalized convex functions. [results] the equivalent relations between F-convex (quasiconvex) functions and convex (quasiconvex) functions are pointed out. Furthermore, the equivalent characterizations of gradient correlation for differentiable F-convex (quasiconvex) functions are given. Finally, as an application, some discriminant methods of GA-convex function are given by using the obtained results. [conclusion] some basic results of convex analysis are uniformly extended to generalized convex functions, and the problem of distinguishing differentiable F-convex (quasiconvex) functions is solved.
【作者单位】：佳木斯大学理学院数学系;
【基金】：佳木斯大学科学技术研究重点项目(No.12Z1201517) 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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