Target Function

Rosenbrock: f(x) = 100(x2-x1^2)^2 + (1-x1)^2

Initial guess

The initial point is either (1.2, 1.2) or (-1.2, 1). To start at a different initial guess, change lines 105/106.

Minimization Algorithm

Uses either Newton's Method or Gradient Descent.

Both of these algorithms will return three values:

1. a vector representing the minimizer
2. x_points: an array of the x1 coordinates of the points taken by the algorithm at each iteration
3. y_points: an array of the x2 coordinates of the points taken by the algorithm at each iteration

Step Size Selection

Backtracking line search with initial α = 1.

Step Size Values

The file a_k.csv contains the a_k values of the algorithms through every iteration. The first column is for the newton's method when the initial point is (-1.2,1.0). The second column is newton's method when initial point is (1.2,1.2). The third column is gradient descent when starting at (1.2,1.2) and the final column is gradient descent when starting at point (-1.2,1.0).

Plots

The file grad_desc_x_-1.2_y_1.png corresponds to gradient descent when the initial starting point is (-1.2,1) The file grad_desc_x_1.2_y_1.2.png corresponds to gradient descent when the initial starting point is (1.2,1.2) The file newton_x_-1.2_y_1.png corresponds to newtons method when the initial starting point is (-1.2,1) The file newton_x_1.2_y_1.2.png corresponds to newtons method when the initial starting point is (1.2,1.2)