用线性泛函表达两个凸集距离的一些公式

Some formulae on the distance of two convex sets represented by linear functionals

获得用线性泛函表达最近距离 ρ(F ,G)的一系列公式 ,并讨论了他们的多种形式 这是关于两个集近渡点理论及带距离性分离定理一系列工作的推进 得到了特殊情形下的单点集到凸集的最佳逼近渡公式 ,与已知结果相吻合 最后考虑了共轭空间X

Some formulae of shortest distance ρ(F,G) represented by extreme values of linear functionals are obtained and various of them are discussed. In particular, it derives the formulae of best approximation of a single point to a convex set, which coincide with some well known results. By the way, the problem is considered about the formulae of the distance of two convex sets in the conjugate space X . [