[SOLVED] CSE-CE-ISyE524 Homework 8- Lagrange duality

1. Consider the problem
) subject to 1 − x1 ≤ 0.
(a) Write down the solution of this problem and the optimal primal value p∗.
(b) Derive the Lagrangian dual function g(λ) for λ ∈R.
(c) Find the solution of the Lagrangian dual problem maxλ≥0 g(λ) and write down the optimal dual objective d∗.
(d) Is the Slater condition satisfied for this problem? Does strong duality hold, that is, p∗ = d∗?
2. Consider the problem
min x1x2 subject to .
Repeat parts (a)-(d) of Question 1 for this problem.
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