Optimization code : Solution Essays

This programming assignment asks you to implement the barrier method for convex optimization problems subject to both equality and inequality constraints (Algorithm 11.1 in the textbook). For the stopping criteria, you can use ||∇f(x)||2 ≤ , where = 0.00001. 1. (20 pts) Apply your implementation to the following optimization problem. minimize1 x1 + 1 s.t. x2 + 1 x3 x1 +x2 ≤ 2; x2 +x3 ≤ 2; x3 +x1 ≤ 2; xj ≥ 0,1 ≤ j ≤3. You are to use the starting point (0.5,0.5,0.5), which is strictly feasible. Show the rst 5 and last 5 Newton iterations of the rst centering step (refer to the rst part for information to be demonstrated). Information to be shown for each Newton iteration are the same as in your rst programming assignment, with the addition of two values: the value of t, and the iteration number of the centering steps. Also show the rst 5 and last 5 Newton iterations of the last centering step. You also need to show the values of α, β (used in line search), µ (used in the barrier method), and . 2. (20 pts) Apply your implementation to the following optimization problem. maximize log(x1) + log(x2) + log(x3) s.t. x1 +x2 ≤ 2; x2 +x3 ≤ 2; x3 +x1 ≤ 2; xj ≥ 0,1 ≤ j ≤3.