Randomized Nyström Preconditioned Interior Point-Proximal Method of Multipliers (Nys-IP-PMM)

This code base uses the Julia Language and DrWatson to make a reproducible scientific project named

Nys-IP-PMM

The project is a companion code for the article "Randomized Nyström Preconditioned Interior Point-Proximal Method of Multipliers", authored by Ya-Chi Chu, Luiz-Rafael Santos, Madeleine Udell. We provide the instructions to reproduce the experiments in the paper.

Preliminary steps

0. Open a Julia console and run the following commands:

   julia> using Pkg
   julia> Pkg.add("DrWatson") # install globally, for using `quickactivate`
   julia> Pkg.activate("path/to/this/project")
   julia> Pkg.instantiate()
   

Large-Scale portfolio optimization experiment (Section 5.1)

1. Run the script scripts/Portfolio/run_portfolio.jl. It will generate the data, run the experiments for the synthetic portfolio optimization problem, and save the results in the folder Portfolio/results/risk_model.
2. Run the script notebooks/Portfolio_analysis/get_demonstrate_results.jl. It will copy the latest 6 results in Portfolio/results/risk_model to notebooks/Portfolio_analysis/demonstrate_results folder for plotting.
3. Run the notebook notebooks/Portfolio_analysis/plotting.ipynb to generate the plot in the paper.

SVM experiments (Section 5.2)

0. Download the required support vector machine (SVM) datasets to a new folder data by running the file scripts/SVM/SVM_data_download.jl.

SVM on all datasets (Section 5.2.1)

1. Run the script scripts/SVM/SVM_run_tests.jl. It will preprocess datasets, run the experiments, and save the results as .csv files under the folder SVM/results/[dataset_name]/IPPMM.
2. Run the script scripts/SVM/SVM_collect_results.jl to collect all the results in the folder SVM/results and save them as a summary .csv file under the folder SVM/results/summary.

Condition numbers at different IP-PMM stages (Section 5.2.2)

0. The condition numbers are saved under notebooks/SVM_analysis/condnum_rank.
1. Run the section "Condition Number v.s. Rank" in the notebook notebooks/SVM_analysis/plotting.ipynb to generate the plot in the paper.

Running time experiments (Section 5.2.3)

1. Run the section "Time v.s. Rank" in the notebook notebooks/SVM_analysis/plotting.ipynb to generate the plot in the paper.