毕业论文外文翻译-凸函数的性质与应用.doc

外文翻译凸函数的性质与应用学 院：理学院专 业：数学与应用数学姓 名： 学 号： 指导教师： 1. Introduction Convex is a very vivid adjectives according to the dictionary explains the meaning of the projection is higher than the surrounding exactly as shown by the shape of the word, the very image of very specific.  This study is "convex function" of some properties, as the name implies, this function of the geometry is a "higher than the surrounding" function. Speaking of "higher than the surrounding" naturally refers to a certain point geometry nature, but that argument is very vague, because "low" is relative, "around" has yet to be defined. then in mathematics we can not adopt this kind of visual language to describe the function of this image geometry with of this article we will abstract geometric sense this feature, use the language of mathematics to describe the function with such features - convex function. Convex function in mathematics is a kind of very important functions, convex function was first defined in 1905 by the Danish mathematician Jensen given, the development has a convex function of applied more widely, especially in convex analysis has become basis of many branches of applied mathematics, it is mathematical analysis, function theory, functional analysis, optimization theory, especially in terms of function graph depicting the derivation and inequality have very widely used. convex function has a good nature , to reflect on the image of intuitive problem-solving approach for the use of Shuoxingjiege provided for convenience and utility, the other has a convex function and inequality inherent in the relationship, and many take advantage of some properties of the inequality problem convex function, you can get a good solved .1.绪论凸是一种很形象的形容词.按词典中的解释,凸的含义是高于周围完全如同这个字所表现出的形状，很形象很具体. 本文研究的是“凸函数”的一些性质,顾名思义,这种函数几何形状上就是一种“高于周围”的函数.说到“高于周围”,自然是指某个几何图形的某个点的性质.但是这样的说法很模糊,因为“高低”是相对的，“周围”也有待明确.那么在数学中我们就不能再用这种直观的语言来描述带有这种图像几何形状的函数了，本文中我们将从几何意义上抽象出这种特点，用数学的语言去描述带有这类特点的函数凸函数 凸函数在数学中是一类非常重要的函数, 凸函数的定义最早是在1905年由丹麦数学家Jensen给出的,发展至今函数的凸性应用越来越广,特别是凸分析现已成为应用数学许多分支的基础,它在数学分析、函数论、泛函分析、最优化理论中,特别是在函数的图形描绘和不等式的推导方面都有很广泛的运用.凸函数有着很好的性质，在图像上的反映直观，为利用数形结合的方法解题提供了方便而实用工具,另外凸函数与不等式以有着先天的关系，很多不等式问题利用凸函数的一些性质，可以得到很好的解决. Research on the convex function more and more over time, the definition of convex function are also diverse, this paper first convex variety of ways to define a function to sort induction, and then study the relationship between them both the same definition of the concept, that there must be contact with each other in this paper discusses the strength immediately equivalence between them. elaborated after some good properties of convex functions in this article, along with examples to learn about the convex Some simple applications function. Since the convex and concave function is sometimes referred to as a convex function, so convex function discussed in this article are only convex function.2. Convex function defined2.1 Several different ways to define convex function Definitions 1 Let be defined on the interval , called in on the is a convex function, if and only if: ，there If the formula, "" into "", is the strict definition of a convex function if "" into "" or "", respectively concave function is defined and strictly concave function Since the convex and concave is a dual concept. What conclusion for one, also corresponding to another conclusion. 关于凸函数的研究越来越多,随着时间的发展,凸函数的定义也多种多样,本文先凸函数的多种定义方式进行整理归纳, 然后对他们之间的关系进行研究,既是同一概念的定义,那彼此间必有联系.在本文中紧接着讨论了它们之间的强弱等价关系.之后在本文中阐述了凸函数一些很好的性质,并附以例题来学习有关凸函数的一些简单应用. 由于上凸函数和下凸函数有时统称为凸函数，所以本文所讨论的凸函数都是只下凸函数.2.凸函数的定义2.1凸函数的几种不同定义方式定义1 设在区间上有定义，在上称为是凸函数，当且仅当：，有 若式中，“”改成“”，则是严格凸函数的定义.若“”改成“”或“”，则分别是凹函数与严格凹函数的定义 由于凸与凹是对偶的概念，对其中一个有什么结论，对另一个亦有相应的结论In this paper, we mainly to define the nature and the simple application of convex functions related discussions with their respective corresponding concave function can be obtained. This is the most basic definition of a convex function definitions.在这篇论文里，我们主要对凸函数的定义性质及简单应用进行相关讨论，与其对应的凹函数可以相应得到这是凸函数定义中最基础的定义。3