| 凸函数的共轭函数的几何解释 |
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| 引用本文： | 董玉林,邵福波,夏尊铨.凸函数的共轭函数的几何解释[J].辽宁师范大学学报(自然科学版),2013(1):11-14. |
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| 作者姓名： | 董玉林 邵福波 夏尊铨 |
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| 作者单位： | 山东科技大学信息科学与工程学院;青岛滨海学院信息工程学院;大连理工大学数学科学学院 |
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| 基金项目： | 国家自然科学基金项目(11171049);山东科技大学春蕾计划资助(2008AZZ049) |
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| 摘 要： | 在凸分析和凸优化中,凸函数的共轭函数是一个非常重要的概念.给定一个凸函数,要求出该函数的共轭函数,并对共轭函数的图像有一个直观清晰的了解并不容易.而一个函数的图像对理解该函数的性质非常重要.基于凸分析中凸函数及其共轭函数的概念及性质,给出了共轭函数的几何解释.这种解释有助于对共轭函数的概念及其性质的理解.
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| 关 键 词： | 共轭函数 凸函数 凸优化 |
Geometric interpretation of conjugates of convex functions |
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| DONG Yulin,SHAO Fubo,XIA Zunquan.Geometric interpretation of conjugates of convex functions[J].Journal of Liaoning Normal University(Natural Science Edition),2013(1):11-14. |
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| Authors: | DONG Yulin SHAO Fubo XIA Zunquan |
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| Institution: | 1.College of Information Science and Technology,Shandong University of Science and Technology,Qingdao 266510,China; 2.Institute of Information Engineering,Qingdao Binhai University,Qingdao 266555,China; 3.School of Mathematical Sciences,Dalian University of Science and Technology,Dalian 116024,China) |
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| Abstract: | Conjugates of convex functions is an important concept in convex analysis and convex opti- mization. Given an convex function, it is not easy to obtain the conjugate of the function, and have clear imagination of the graph of the conjugate function. But the graph of the function can help us to understand the properties of the function. This paper, based on the properties of the convex function and its conjugates function, presents the geometric interpretation of the conjugates of convex func- tion. This interpretation can help us to understand the concept of the conjugate. |
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| Keywords: | conjugates of convex functions convex function convex optimization |
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