# A code example on primal-dual algorithm for LP

**URL:** <https://discourse.julialang.org/t/a-code-example-on-primal-dual-algorithm-for-lp/128148>\
**Category:** Offtopic\
**Tags:** examples\
**Created:** [April 17, 2025, 5:08am UTC](https://discourse.julialang.org/t/a-code-example-on-primal-dual-algorithm-for-lp/128148 "2025-04-17T05:08:24Z")\
**Posts on this page:** 1\
**Showing post:** 15

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**Author:** ![WalterMadelim](https://avatars.discourse-cdn.com/v4/letter/w/3e96dc/32.png) [@WalterMadelim](https://discourse.julialang.org/u/WalterMadelim)\
**Post date:** [April 26, 2025, 8:22am UTC](https://discourse.julialang.org/t/a-code-example-on-primal-dual-algorithm-for-lp/128148/15 "2025-04-26T08:22:49Z")

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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 I’m currently having trouble selecting [it](https://discourse.julialang.org/t/what-is-a-recommended-way-to-solve-a-linear-equation/128420). 😇

```julia
******************************************************************************
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.

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