1 Form the Dual and form the dual of the dual Consider the following LP: min s.t. 3x12x2 + x3 -x1x₂ + 2x3 + 2x4 ≥ 10 - 3
Posted: Mon Jul 11, 2022 12:07 pm
- 1 Form The Dual And Form The Dual Of The Dual Consider The Following Lp Min S T 3x12x2 X3 X1x 2x3 2x4 10 3 1 (77.87 KiB) Viewed 22 times
1 Form the Dual and form the dual of the dual Consider the following LP: min s.t. 3x12x2 + x3 -x1x₂ + 2x3 + 2x4 ≥ 10 - 3x₁ + x₂ - 4x3 x4 = 5 - x₁ + 2x₂ - 2x3 + x4 ≤ 4 X1 ≤ 0, X2, X3 ≥ 0, 4 free (a) Form a Lagrangian relaxation problem by relaxing the three constraints. The answer should be a minimization problem in the variable. (b) Write down the the closed form solution of this Lagrangian relaxation problem. (c) Write down the dual maximization problem. (d) Denote the dual maximization problem obtained above as (D). Now formulate the dual of (D) using Lagrangian relaxation. You should develop a similar procedure, except here you need to obtain the best upper bound of (D). Compare the dual of the dual with the primal. Are they equivalent?