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 College
lecture4 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 ( ) ( ) =
2S.C. for cost function Differentiable function o(w, g) satisfied HD1 of w Concave of w ° Non-decreasing of w Nonnegative for w≥0,q≥0 Then o(w, q)is the cost function definite by the tech.ofv(q)={x∈9w·x≥p(w,q)} lecture 4 for Chu Kechen Honors College
lecture4 for Chu Kechen Honors College 2.S.C. for cost function ▪ Differentiable function satisfied: • HD1 of w • Concave of w • Non-decreasing of w • Nonnegative for . ▪ Then is the cost function definite by the tech. of ( , ) w q w 0, 0 q ( , ) w q 1 ( ) { : ( , )} n V q q − = + x w x w