Homework 8: Lagrange duality

Description

1. Consider the problem

	1	2	2
min		(x	+ x ) subject to 1	x		0:
	2
x1;x2		1	2	1

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

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

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

1. 4. 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.

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