| Step 1: Set the initial value(Θ̃0) with Θ̃p1,10 (without Phase I, randomize the initial value) |
| Step 2: Iterate nonlinear optimization procedure (Convergence limit: Tolerance ≤ 0.00001) |
| - Obtain the search direction (qk) with Hessian matrix(Hk, k: iteration number): |
| q k = − H k ∇ f # ( T F , Θ , Θ ˜ k , Φ ) , q k ∈ ℛ 9 , H k ∈ ℛ 9 x 9 , ∇ f # ∈ ℛ 9 |
| - Calculate the step size(αk) by using golden section search technique: |
| α k = arg α m i n f # ( T F , Θ , Θ ˜ k + α q k , Φ ) |
| - Update new solution: Θ ˜ k + 1 = Θ ˜ k + α k q k |
| - Update Hessian matrix with the difference of gradients: |
| H k + 1 ← H k , α k q k , ∇ f # ( T F , Θ , Θ ˜ k + 1 , Φ ) − ∇ f # ( T F , Θ , Θ ˜ k , Φ ) |
| Step 3: Find the optimal solution → Θ ˜ o p t = Θ ˜ p 2 |