Here is the instruction to run the Matlab code in this folder.

The loss_gradient.m file calculate the vector F(z).

The loss_hessian.m file calculate the Jacobian matrix F'(z).

The RandOrthMat.m file generate the random orthogonal matrix with dimension n*n.

The main_iteration.m file generate the plots with different algorithms. The y-axis is the ratio between the square of the norm of F(z_T) and the square of the norm of F(z_0). The x-axis is the number of iterations T.

The main_iteration.m file generate the plots with different algorithms. The y-axis is the ratio between the square of the norm of F(z_T) and the square of the norm of F(z_0). The x-axis is running time of the algorithms measured in seconds.

We compare the performance of Adaptive Second Order Method with Parameter L, Parameter-free Adaptive Second Order Method, Homotopy Inexact Proximal-Newton Extragradient Method and Generalized Optimistic Second Order Method. Please check the numerical experiments section in the paper for the reference of these different algorithms.