拟凸函数的性质及应用
毕业论文关键词 拟凸函数 上半连续 水平集 开凸锥 严格拟凸
Title Properties and applications of the quasi-convexfunction
Abstract Convexity is a very important property of the functions.It plays an important role in theoptimization and has a very important position in the field of research function.So far,we havenot only gotten a lot of research about the nature of convex function,but also gotten lots ofachievements of practical application.And we research concave and convex nature offunction,because it is very useful to the mathematical Analysis.Convex-Function plays a veryimportant role in the mathematical Analysis especially in function’s graph-depicting and theproof of inequality.Convex-function has good properties.It not only has widely used theory,butalso has widely use in practical application.However,,in practice many functions do not meetstrict convexity condition due to the convexity of the conditions is relatively high.So,we needpromote the nature of the convex-function.It is not only a theoretical demand, but also thepractical application needs .This paper focuses on researching a class of extension of convex function -- quasi-convexfunctions. Quasi-convex function is an important content of mathematical function whichresearches Convexity of . Because of the high requirements of the convex functions. In manyproblems of mathematical programming and economics the convex function can not be qualifiedfor the next research work when the condition is too strong convexity,at this time we need to usequasi-convexity. Quasi-convex function requires weak than convex function. In many areaswhich the convex functions can not be involved, maybe the Quasi-convex function has beenwell used. And most of the results of convex function can be generalized to the quasi-convexfunction . Therefore, the study of the quasi-convex function’s nature is very important. The studyof Quasi-convex function direction constitutes one of the research today mathematicalprogramming problem is an important direction.
Keywords Quasi convex function;Upper Semi-continuous Mappings; Level Set;Open convex cone;Strictly quasi-convex.
目次
1绪论1
2凸函数的预备知识5
2.1凸函数的定义和几何意义7
2.2凸函数与Jensen不等式8
2.3凸函数与Hadamard不等式10
3拟凸函数12
3.1拟凸性和单调性14
3.2连续性15
3.3可微性16
3.4拟凸函数与Hadamard不等式18
3.5拟凸函数与土凸函数的区别19
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