Linear programming Interior-Point Algorithm.

LIPA is a C++ package designed to solve linear optimization problems using interior-point method.

On it's current state, the project is implemented as a solution to the GeomsScale GSoC 2020 test task.

Download repo with git clone --recursive https://github.com/AndreyBychkov/LIPA.git

If any issues with submodules arise, try checking out this article.

The project strongly depends on BLAS and LAPACK libraries, so make sure you have them in your system. We suggest following guide from Armadillo for general information about installing this dependencies.

We use OpenBLAS as realisation of BLAS + LAPACK bundle. Consider checking it's building manual.

Our steps for CMake + MinGW:

1. cd OpenBLAS
2. mkdir build
3. cd build
4. cmake .. -G "MinGW Makefiles" -DCMAKE_BUILD_TYPE=Release
5. cmake --build . -j --target all

It will produce directory lib in OpenBLAS/build with libopenblas.a in it which we link in Cmake as follows:

target_link_libraries(LIPA ${CMAKE_SOURCE_DIR}/OpenBLAS/build/lib/libopenblas.a)

Replace libraries in function with yours if needed.

Define linear optimization problem as follows:

LinearOptimizationProblem problem = LinearOptimizationProblem(A, b, c);

• Maximization:

LinearOptimizationResult result = problem.maximize(x_0, gamma, mir_err, method);

• Minimization: For minimization replace vector c with negative -c and consider it as maximization problem.

vec c_neg = -c;
LinearOptimizationProblem problem = LinearOptimizationProblem(A, b, c_neg);
LinearOptimizationResult result = problem.maximize(x_0, gamma, mir_err, method);

In LinearOptimizationResult class we store the solution itself as well as utility information like intermediate solutions and the number of iterations.

result.result.print("Solution x:");