Newton-MR

Newton-MR is a second-order Newton-type optimisation algorithms. This python codes is for the paper Convergence of Newton-MR under Inexact Hessian Information.

Authors: 
    Yang Liu, 
    School of Mathematics and Physics, the University of Queensland, Australia.
    contact: yang.liu2(AT)uq.edu.au
    
    Fred Roosta,  
    School of Mathematics and Physics, the University of Queensland, Australia, 
        and International Computer Science Institute, Berkeley, USA.
    contact: fred.roosta(AT)uq.edu.au

All optimisation algorithms can be found at optim_algo.py To regenerate figures of the above paper...

Run main_Fraction.py   to regenerate Figure 2.
Run main_Softmax2nd.py to regenerate Figure 3.
Run main_Softmax1st.py to regenerate Figure 4 and 5.
Run main_MRvsCG.py     to regenerate Figure 6 and 7.
Run main_GMM2nd.py     to regenerate Figure 8.
Run main_GMM1st.py     to regenerate Figure 9 and 10.

Reference:

"Convergence of Newton-MR under Inexact Hessian Information".
Authors: Yang Liu, Fred Roosta. ArXiv:1909.06224

"Newton-MR: Newton’s Method Without Smoothness or Convexity".
Authors: Fred Roosta, Yang Liu, Peng Xu, Michael W. Mahoney. ArXiv: 1810.00303