Extremal Problems Related to Gauss-John Position  

作　　者：Ai Jun LI Gang Song LENG 

机构地区：[1]School of Mathematics and Information Science,Henan Polytechnic University [2]Department of Mathematics,Shanghai University

出　　处：《Acta Mathematica Sinica,English Series》2012年第12期2527-2534,共8页数学学报（英文版）

基　　金：Supported by National Natural Science Foundation of China (Grant No. 10971128);Shanghai Leading Academic Discipline Project (Grant No. S30104);Doctoral Fund of Henan Polytechnic University (Grant No. B2011-024)

摘　　要：In this paper, we consider the extremal problem of the ;p-norm： min{;p（TK）, o E TK C L, T E GL（n）}, where K, L are two convex bodies in Rn. Using the optimization theorem of John, we give necessary conditions for K to be in extremal position in terms of a decomposition of the identity. Fhrthermore, the weaker optimization problem, min{（lp（TK））p ： TK C B2n,TK Sn-1 ≠ O,T E GL（n）}, is also considered. As an application, the geometric distance between the unit ball B2n and a centrally symmetric convex body K is obtained.In this paper, we consider the extremal problem of the ;p-norm： min{;p（TK）, o E TK C L, T E GL（n）}, where K, L are two convex bodies in Rn. Using the optimization theorem of John, we give necessary conditions for K to be in extremal position in terms of a decomposition of the identity. Fhrthermore, the weaker optimization problem, min{（lp（TK））p ： TK C B2n,TK Sn-1 ≠ O,T E GL（n）}, is also considered. As an application, the geometric distance between the unit ball B2n and a centrally symmetric convex body K is obtained.

关 键 词：Gauss-John position optimization theorem of John LP-NORM contact pair 

分 类 号：O177.2[理学—数学]