几何凸函数若干问题的探讨毕业论文.doc

几何凸函数若干问题的探讨
摘要
几何凸函数是一类非常重要的函数,广泛应用于数学规划、控制论等领域,它在判定函数的极值、研究函数的图像以及不等式的证明诸方面都有广泛的应用。文章首先探究凸函数这类性质特殊的函数的各种定义及几何意义,探究几何凸函数在不同学科上的应用。讨论了几何凸函数的一些性质,并运用其性质证明若干不等式,介绍函数几何凸性的几种判别方法。
文章证明几何凸性函数的几个生成定理,并给出一元高次多项式函数几何凸性的几个结论,最后给出几何凸函数定义的推广或类似,供进一步研究之用。给出凸集的定义,借助凸集来引入凸函数的几何直观性定义,并借此给出几何凸函数的解析式定义,进行一系列的分析、类比、归纳,用实例说明用几何凸函数解决实际问题的重要意义。
由于几何凸函数理论的广泛性,因此对其理论的研究成果还有待进一步的深入和推广。如何推广函数的凸性概念,使得在更广泛的函数范围内,凸函数的许多重要性质仍然得以保留,凸规则的大多数结果能推广到非凸规则,已构成了数学规划研究领域的当前趋势之一,所以研究几何凸函数的一些定义和性质就显得十分必要了。文章所述内容使我们能够快速获取大量有关几何凸函数的重要内容,从而使解决一类特别繁杂不等式证明、最优化等问题变的别出一格。
关键字:凸函数;几何凸函数;不等式
The Discussion on some Questions of Geometric Convex Function
Abstract
Geometric convex function is a very important function, widely used in mathematical programming, control theory and other fields determine the extremism of the function, the image of the research function and the inequality proof aspects have a wide range of applications. The article first explores the various definitions and geometric meaning of convex function of the nature of the special function to explore the geometric convex function on the different disciplines. Discussed some properties of the geometry of convex function, and use nature to prove certain inequalities on the function of geometric convexity several discriminate methods.
Article to prove the convexity of the function of the geometry of several generation theorems, and several conclusions given a high geometric convexity of a polynomial function. Finally, promotion or similar geometric convex function defined for the purposes of further study. Given the definition of convex sets, with the convex set to the introduction of geometric definition of convex function, and to give the analytical definition of the geometric convex function, a series of analyzes, analogy, induction, illustrated by an example using Geometric Convex Function to solve practical problems of great significance.
Due to the extensive geometric convex function theory, its theoretical research remains to be furth