Let w x1 x2 x3 y1 y2 y3 z1 z2 z3 and the function find the

Question

MATLAB Assignment -

Two independent works or problems to be solved. In problem 2, λ_k, α_k, δ_k, τ , L are very important parameters. So clearly indicate them.

Problem 1 -

Let w = (x₁, x₂, x₃, y₁, y₂, y₃, z₁, z₂, z₃) and the function

Ψ(w) = -√(5.4(y₁ - x₁) - 3(y₂ - x₂))²+(- 3(y₁ - x₁) + 4.67(y₂ - x₂))² + (7.16(y₃ - x₃))²

- √(3.1z₁ + 2z₂ + 1.6y₁ + y₂ + 1)²+(2z₁ + 3.6z₂ + y₁ + 1.6y₂ - 2)²+(1.5z₃ + 3.5y₃ + 3)²

Find the minimum value of Ψ(w) where

-x₁ - x₂ - x₃ ≤ -1, 0 ≤ x_i ≤ 1, i = 1, 2, 3

-y₁ - y₂ - y₃ ≤ -1, 0 ≤ y_i ≤ 1, i = 1, 2, 3

-z₁ - z₂ - z₃ ≤ -1, 0 ≤ z_i ≤ 1, i = 1, 2, 3.

Problem 2 - Algorithm

Let x⁰ ∈ R³ be initialazation of the algorithm and

And λ_k, α_k, L and τ be real parameters given by λ_k = 1/(k+50)^1.1 , α_k = 1/2^k, τ = 0.99, L = 100. k ≥ 0, 1, 2, ...

Step 1: Let

Step 2: Let

Step 3:

s^k = α_kx^k + (1 - α_k)z^k.

Step 4: Let

Step 6: Go to step 1.