On Minimum Morm Problem in Normed Space

Hahn-Banach continuation is important for us to research optimization theory on normed space.At the same time,it is a powerful tools to research minimum norm.Minimum norm problem in Hilbert can be excellently solved through projection theorem.However,it is complex on the ordinary normed space and convex set.In ordinary normed space,minimum norm problem can work out by Duality theorem,but involving two different normed spaces.From another point of view,this paper discuss the minimum norm through formal geometry of Hahn-Banach theorem.It is easy to get out of trouble in considering two different normed spaces.In addition, formal geometry of Hahn-Banach theorem is associated with related objects in original space with objects in dual space,so geometric interpretation is given for the problem of minimum norm.