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. 1 of 1
