Homework 8: Lagrange duality

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Consider the problem 1 2 2 min (x + x ) subject to 1 x 0: 2 x1;x2 1 2 1 Write down the solution of this problem and the optimal primal value p . Derive the Lagrangian dual function g( ) for 2 R. Find the solution of the Lagrangian dual problem max 0…

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  1. Consider the problem

1

2

2

min

(x

+ x ) subject to 1

x

0:

2

x1;x2

1

2

1

    1. Write down the solution of this problem and the optimal primal value p .

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

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

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

  1. Consider the problem

min x1x2 subject to x21 + x22 1 0:

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

1 of 1

Homework 8: Lagrange duality
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