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Chapter 3. Duality in convex optimization Version: 22-10-2010
 

Summary: Chapter 3. Duality in convex optimization
Version: 22-10-2010
3.1 Lagrangean dual
Recall the program (J = {1, . . . , m})
(CO) min
xC
f(x) | gj(x) 0, j J
with convex functions f, gj, a convex set C, minimal value
v(CO), feasible set F, the Lagrangean function:
L(x, y) = f(x) +
m
j=1
yjgj(x) , x C , y 0
L(x, y) is convex in x and linear in y.
CO p 1
Defining
(y) := inf
xC
{f(x) +
m

  

Source: Al Hanbali, Ahmad - Department of Applied Mathematics, Universiteit Twente

 

Collections: Engineering