1. duality in mathematics Support function: (infimum) k(p)=nfpx:x∈K} ux(p) given an alternative description for K K={X∈9”:px≥/k(p) for every p} Proposition8: Pk(p)is HD1 and concave See thefig lecture 4 for Chu Kechen Honors Collegelecture4 for Chu Kechen Honors College 1.Duality in mathematics ▪ Support function: (infimum) ▪ given an alternative description for K. ▪ Proposition8: is HD1 and concave. See the fig. inf{ : }  K ( ) =  p px x K K  ( ) p { : for every } n K =   ( ) K x px p p  K  ( ) p