Experiments for Optimal Low-Rank Matrix Completion: Semidefinite Relaxations and Eigenvector Disjunctions

Repository of numerical experiments for the paper Optimal Low-Rank Matrix Completion: Semidefinite Relaxations and Eigenvector Disjunctions.

Use

• Check that you have a valid installation of Mosek, as well as the package OptimalMatrixCompletion.jl (link here) installed.
• The /postprocessing folder contains all postprocessing scripts, that transform raw data into tables and plots that appear in the paper.
  • A list corresponding figure and table numbers in the paper to file names in /postprocessing/tables and /postprocessing/plots is included in /postprocessing/README.md.
• The experiments are grouped by folder, and are in all folders other than /postprocessing.
  • If you would like to run them, run the script.jl files attached in each subdirectory as follows:

    # cd to the subdirectory containing script.jl
    julia script.jl
    

  • These script files were made to run on a distributed computing cluster; if you are running them locally on your machine, change the following lines:

    task_index = parse(Int, ARGS[1]) + 1
    n_tasks = parse(Int, ARGS[2])   
    

    to:

    task_index = 1
    n_tasks = 1
    

    (You can also use other values if you want to run only a subset of the instances.)
  • After execution, the results of individual instances will appear in the corresponding /records subdirectory.