Homework 8: Lagrange duality

    1. Consider the problem

1
2
2



min

(x
+ x )  subject to 1
x

0:

2





x1;x2

1
2
1



        (a) Write down the solution of this problem and the optimal primal value p .

        (b) Derive the Lagrangian dual function g( ) for  2 R.

        (c) Find the solution of the Lagrangian dual problem max 0 g( ) and write down the optimal dual objective d .

        (d) Is the Slater condition satis ed for this problem? Does strong duality hold, that is, p = d ?



    2. Consider the problem
min x1x2    subject to x21 + x22    1    0:

Repeat parts (a)-(d) of Question 1 for this problem.








































1 of 1