MATLAB Version

This page shows how to use the MATLAB interface of HPR-LP: run demos, build custom problems, adjust solver settings, and interpret results.

Running examples

The demo LP problem is:

Test problem (LP)

The default demo problem we ship is a small linear program of the form

\[\begin{split} \begin{aligned} \min \quad & - 3 x_1 - 5 x_2\\ \text{s.t.} \quad & x_1 + 2 x_2 \le 10, \\ & 3 x_1 + x_2 \le 12, \\ & x_1 \ge 0, \\ & x_2 \ge 0. \end{aligned} \end{split}\]

Usage 1: Test Instances in MPS Format

Setting Data and Result Paths

Before running the scripts, please modify run_single_file.m or run_dataset.m in the scripts directory to specify the data path and result path according to your setup.

Running a Single Instance

To test the script on a single instance (.mps file):

% Set parameters (optional)
params = HPRLPParameters();
params.stoptol = 1e-4;
params.time_limit = 3600;

% Solve from MPS file
results = runFile('your_problem.mps', params);

% Check results
fprintf('Status: %s\n', results.output_type);
fprintf('Objective: %.6e\n', results.primal_obj);

Running All Instances in a Directory

To process all .mps files in a directory:

% Configure parameters
params = HPRLPParameters();
params.stoptol = 1e-4;
params.time_limit = 600;

% Run on all files in the directory
runDataset('/path/to/mps/files', '/path/to/results', params);

Usage 2: Define Your LP Model in MATLAB Scripts

Example 1: Define an LP Instance Directly in MATLAB

This example demonstrates how to construct and solve a linear programming problem directly in MATLAB without relying on MPS files.

run('demo/demo_Abc.m')

The script demonstrates:

Direct matrix-based LP formulation
Setting up the problem: min c'*x subject to AL ≤ A*x ≤ AU, l ≤ x ≤ u
Solving with HPR-LP
Accessing solution values

Example problem from the demo:

% Define LP: min -3*x1 - 5*x2
%     s.t. -x1 - 2*x2 >= -10
%          -3*x1 - x2 >= -12
%          x1 >= 0, x2 >= 0

A = sparse([-1 -2; -3 -1]);
AL = [-10; -12];
AU = [Inf; Inf];
c = [-3; -5];
l = [0; 0];
u = [Inf; Inf];
obj_constant = 0.0;

params = HPRLPParameters();
params.stoptol = 1e-4;

result = runAbc(A, c, AL, AU, l, u, obj_constant, params);

fprintf('Objective value: %.10f\n', result.primal_obj);
fprintf('x1 = %.10f\n', full(result.x(1)));
fprintf('x2 = %.10f\n', full(result.x(2)));

Parameters

Below is a list of the parameters in HPR-LP along with their default values and usage:

Parameter	Default Value	Description
`time_limit`	`3600`	Maximum allowed runtime (seconds) for the algorithm.
`stoptol`	`1e-4`	Stopping tolerance for convergence checks.
`max_iter`	`intmax`	Maximum number of iterations allowed.
`check_iter`	`150`	Number of iterations to check residuals.
`use_Ruiz_scaling`	`true`	Whether to apply Ruiz scaling.
`use_Pock_Chambolle_scaling`	`true`	Whether to use the Pock-Chambolle scaling.
`use_bc_scaling`	`true`	Whether to use the scaling for b and c.
`print_frequency`	`-1` (auto)	Print the log every `print_frequency` iterations.

Result Explanation

After solving an instance, you can access the result variables as shown below:

% Example from demo/demo_Abc.m
fprintf('Objective value: %.10f\n', result.primal_obj);
fprintf('x1 = %.10f\n', full(result.x(1)));
fprintf('x2 = %.10f\n', full(result.x(2)));

Category	Variable	Description
Iteration Counts	`iter`	Total number of iterations performed by the algorithm.
	`iter_4`	Number of iterations required to achieve an accuracy of 1e-4.
	`iter_6`	Number of iterations required to achieve an accuracy of 1e-6.
	`iter_8`	Number of iterations required to achieve an accuracy of 1e-8.
Time Metrics	`time`	Total time in seconds taken by the algorithm.
	`time_4`	Time in seconds taken to achieve an accuracy of 1e-4.
	`time_6`	Time in seconds taken to achieve an accuracy of 1e-6.
	`time_8`	Time in seconds taken to achieve an accuracy of 1e-8.
	`power_time`	Time in seconds used by the power method.
Objective Values	`primal_obj`	The primal objective value obtained.
	`gap`	The gap between the primal and dual objective values.
Residuals	`residuals`	Relative residuals of the primal feasibility, dual feasibility, and duality gap.
Algorithm Status	`output_type`	The final status of the algorithm: - `OPTIMAL`: Found optimal solution - `MAX_ITER`: Max iterations reached - `TIME_LIMIT`: Time limit reached
Solution Vectors	`x`	The final solution vector `x`.
	`y`	The final solution vector `y`.
	`z`	The final solution vector `z`.