LIPSOL (Linear-programming Interior-Point SOLvers) is a software implementation of a primal-dual infeasible-interior-point algorithm for large-scale linear programming problems. It is designed to take advantage of MATLAB's sparse-matrix functions and external interface facilities, as well as existing Fortran sparse Cholesky codes. LIPSOL aims to provide simplicity, versatility, and performance comparable to efficient Fortran or C codes for solving large-scale linear programming problems under the MATLAB environment.
In MATLAB, the 'interior-point-legacy' method for linear programming is based on LIPSOL, which is a variant of Mehrotra's predictor-corrector algorithm, a primal-dual interior-point method. This method is used for solving linear programming problems in MATLAB, and it involves preprocessing steps and iterations to find the optimal solution.
For reference you can check :
Solve linear programming problems: https://in.mathworks.com/help/optim/ug/linprog.html
Interior-Point Methods: https://www.mcs.anl.gov/research/projects/otc/InteriorPoint/abstracts/Zhang-4.html
