Subsampled Riemannian trust-region (RTR) algorithms

Authors: [Hiroyuki Kasai]http://kasai.comm.waseda.ac.jp/kasai/) and Bamdev Mishra

Last page update: June 20, 2019

Latest library version: 1.1.0 (see Release notes for more info)

Introduction

The package contains a MATLAB code presented in the report "Inexact trust-region algorithms on Riemannian manifolds" by Hiroyuki Kasai and Bamdev Mishra in NeurIPS2018 (NIPS2018).

Folders and files

./                      - Top directory.
./README.md             - This readme file.
./run_me_first.m        - The scipt that you need to run first.
./demo.m                - Demonstration script to check and understand this package easily. 
|manopt_mod_solvers/    - Contains modified solvers from manopt.
|manopt-4/              - Contains manopt package.
|problem/               - Problem definition files to be solved.
|propose/               - Contains proposed algorithm files.
|tools/                 - Contains data generation scripts.
|docs/                  - PDF files of NeurIPS paper and poster.

First to do

Run run_me_first for path configurations.

%% First run the setup script
run_me_first; 

Demonstration

Run demo for a simple demonstartion.

%% Run a demonstration script
demo; 

This script demonstrates a case study of using the proposed Subsampled-RTR algorithm (Sub-H-RTR) on a small PCA problem instance. Below is the results of an optimality gap vs. iteration number and time [sec].

Performance results (from paper):

• PCA problem

• Matrix completion problem

Cite

Please cite our paper if you use this code in your own work.

@conference{Kasai_NeurIPS_2018,
    Author = {Kasai, H. and Mishra, B.},
    Booktitle = {NeurIPS},
    Title = {Inexact trust-region algorithms on {R}iemannian manifolds},
    Year = {2018}
}

License

(c) 2017-2019 Hiroyuki Kasai (kasai at is dot uec dot ac dot jp) and Bamdev Mishra (bamdevm at gmail dot com).

Confirmed operating environment:

• This code has been checked on Mac OS (64 bits) under
  • MATLAB 8.2.0.701 (R2013b)
  • MATLAB 9.1.0.441655 (R2016b)
  • MATLAB 9.4.0.813654 (R2018a)
• Note that RTRMC may not work properly in some environments due to its Mex-files.

Problems or questions

If you have any problems or questions, please contact the author: Hiroyuki Kasai (email: hiroyuki dot kasai at waseda dot jp).

Release Notes

• Version 1.1.0 (June 20, 2019)
  • Added initial codes.
• Version 1.0.0 (Nov. 24, 2018)
  • Initial version.