A code example on primal-dual algorithm for LP

Offtopic
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People find established optimization problems need a solver (e.g. Ipopt).
But it maybe somewhat astonishing that solving Ax = b itself sometimes need a solver also, and Iā€™m currently having trouble selecting it. :innocent:

******************************************************************************
This program contains Ipopt, a library for large-scale nonlinear optimization.
 Ipopt is released as open source code under the Eclipse Public License (EPL).
         For more information visit https://github.com/coin-or/Ipopt
******************************************************************************

This is Ipopt version 3.14.17, running with linear solver MUMPS 5.7.3.

I thought MUMPS was an LP solver, which is an illusion.
It is a Ax = b solver.