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Symmetry Function Induced by a Convex Body 被引量：1

Symmetry Function Induced by a Convex Body
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摘要 这份报纸显示出凸的身体在一个正常线性空格导致的对称功能的一些性质。在对称功能之间的一些关系由凸的身体导致了，凸的身体功能的 Minkowski 被介绍。 This paper shows some properties of symmetry function induced by a convex body in a normal linear space. Some relationships between symmetry function induced by a convex body and Minkowski functional of the convex body are presented.
作者 HUANG Long-guang
机构地区 School of Sciences
出处 《Chinese Quarterly Journal of Mathematics》 CSCD 2011年第1期1-6,共6页 数学季刊（英文版）
基金 Supported by the Natural Science Foundation of China（10771086） Supported by the Natural Science Foundation of Fujian Province（S0650021）
关键词 凸的身体 对称功能 凹面 Minkowski 功能 convex body symmetry function concave Minkowski functional
分类号 O221 [理学—运筹学与控制论]
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参考文献4

  • 1GRUNBAUM B.Measures of Symmetry for Convex Sets.In:Convexity,Proceedings of Symposia in Pure Mathematics[C].Providence:American Mathematical Society,1963:233-270.
  • 2RENEGAR J.A Mathematical View of Interior-Point Methods in Convex Optimization,MPS-SIAM Series on Optimization[M].Philadelphia:Society for Industrial and Applied Mathematics,2001.
  • 3XIA Dao-xing,YANG Ya-li.An Introduction to the Linear Topological Space[M].Shanghai:Shanghai Science and Technology Publishers,1986.
  • 4SHI Shu-zhong.Convex Analysis[M].Shanghai:Shanghai Science and Technology Press,1990.

同被引文献11

  • 1EA YOUNESS. On E-convex sets, E-convex functions and E-convex programming[J]. Journal of Optimiza?tion Theory and Applications, 1999, 102(3): 439-450.
  • 2YANG XM. On E-convex sets, E-convex functions and E-convex programming[J]. Journal of Optimization Theory and Applications, 2001, 109: 699-704.
  • 3DI DUCA, LUPSA L. On the E-epigraph of an E-convex function[J]. Journal of Optimization Theory and Applications, 2006, 129(2): 341-348.
  • 4J SHEIBA GRACE, P THANGAVELU. E-convex programming[J]. Journal of Mathematics, Statistics and Allied Fields, 2009, 3(1): 1-2.
  • 5SYAU YR, LEE ES. Some properties of E-convex functions[J]. Applied Mathematics Letters, 2005, 18: 1074-1080.
  • 6RAPCSAK T. Smooth Nonlinear Optimization in lRn[M]. Springer: Kluwer Academic Amsterdam, 1997.
  • 7UDRISTE C. Convex Functions and Optimization Methods on Riemannian Manifolds[M]. Springer: Kluwer Academic Amsterdam, 1994.
  • 8IQBAL A, ALI S, AHMAD I. On geodesic E-convex sets, geodesic E-convex functions and E-epigraphs[J]. Journal of Optimization Theory and Applications, 2012, 155: 239-251.
  • 9ZHAN Yi, LI Ze-min. E-convex Sets, E-convex Functions and E-convex Programming in Linear Space[D]. Chongqing: College of Mathematics and Physics of Chong-qing University, 2006.
  • 10BURAGO D, BURAGO Y, IVANOV S. A Course in Metric Geometry[M]. America: American Mathematical Society, 2001.

引证文献1

Chinese Quarterly Journal of Mathematics
2011年 第1期

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