1. duality in mathematics Duality theorem: K is nonempty closure, and its support function ux() is differentiable at p, then there is only onexe K, that px=HK(p)and Vuk(p)=x lecture 4 for Chu Kechen Honors Collegelecture4 for Chu Kechen Honors College 1.Duality in mathematics ▪ Duality theorem: K is nonempty closure, and its support function is differentiable at , then there is only one , that See the fig. K  ( ) p p x  K and K K p x = p p x  ( )  ( ) =  