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[Help-glpk] glp_simplex() behavior when no primal feasible solution is a

From: Karol Rydzewski
Subject: [Help-glpk] glp_simplex() behavior when no primal feasible solution is available
Date: Mon, 20 Aug 2018 00:01:37 +0200
User-agent: Mozilla/5.0 (Windows NT 10.0; WOW64; rv:52.0) Gecko/20100101 Thunderbird/52.9.1


I am using GLPK in version 4.60 and I trying to solve(find min and max)
an inconsistent and/or overdetermined systems. This is done on purpose as
this is the nature of an environment that I am modelling. To my positive
surprise, glp_simplex(default settings) method returns some solutions to such 
after reporting that "LP HAS NO PRIMAL FEASIBLE SOLUTION".
Unfortunatelly, it is not clear to me, what is the algorithm that GLPK executes 
get these solutions in such cases. I went through some documentation and
searched internet but I haven't found definitive answers. I am not an
expert on LP and reverse engineering is time-consuming for me. Can you
provide me steps that GLPK runs to get the results? These can list of
methods you use, some mathematical theorems or an example of operations
with comments, etc.

Just to give a very primitive example of what my problem is, I can have two 
constrains like this:
I run glp_simplex() where I try to find min and max value for objective 
function x. Let me know if you need some more complex example I run.

Thank you!

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