SimplePDLP

This directory is intended for teaching purpose to illustrate how to design, structure and implement a solver in Julia using an example of PDHG for LP of the form $\min_{x} c^\top x,\ \text{s.t.}\ Ax=b, Gx \le h, l \le x \le u\ .$ It includes reading the data from an .mps file, preconditioning, PDHG, outputting, and examples of solving an instances, plotting the output, and calling from the JuMP interface. The implementation is not to be computationally efficient, but rather include most of the basic components of a first-order method LP solver. A more sophisticated Julia implementation of the algorithm can be found at FirstOrderLp.jl, and the C++ production-level implementation of the algorithm is included in OR-Tools.

Part of the code utilize https://github.com/google-research/FirstOrderLp.jl which originally stated Apache-2.0 as its license and https://github.com/Shuvomoy/SimplePDHG.jl.

Setup

All commands below assume that the current directory is the working directory.

A one-time step is required to set up the necessary packages on the local machine:

$ julia --project -e 'import Pkg; Pkg.instantiate()'

Running instances

$ julia --project script/run_problem.jl [directory_for_problem_instances] [results_directory] [problem_name] [KKT_tolerance] [iteration_limit]

Plotting results

$ julia --project script/plot_result.jl [directory_for_solver_output] [figure_directory] [problem_name]

Example

$ julia --project script/run_problem.jl --problem_folder=./data --output_directory=./output/solver_output --problem_name=neos5 --kkt_tolerance=1e-6 --iteration_limit=20000
$ julia --project script/plot_result.jl --directory_for_solver_output=./output/solver_output --figure_directory=./output/figure --problem_name=neos5

Examples of using JuMP interface to call SimplePDLP

$ julia --project script/jump_example.jl