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After Phase 1, if the sum of artificial variables is zero but there are artificial variables still in the basis, how to get rid of them?

Thanks in advance for any pointer.

HC Luie
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    It would be good to give an example of the situation you ask about. – coffeemath Jun 13 '21 at 03:46
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    I am working on the revised simplex method to tackle a set of NetLib LP problems (https://www.netlib.org/lp/data/index.html). The algo starts phase-1 by adding m artificial variables (m is the # of constraint equations) and construct a LP problem to minimize the sum of artificial variables. In some cases (such as agg.mat where the A matrix dimension is 488x615), I observe that after Phase-1 terminates, there are artificial variables still in the basis and I wonder how to get rid of them. – HC Luie Jun 13 '21 at 14:17
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    OK, HC. Just wondered if there was a relatively small sized problem where this happens so someone could look at a concrete case. There may be such examples in the literature, a link to one would serve. On the other hand maybe someone (more expert than I) can answer your question with the desired thing to do to get rid of such artificial variables, and can answer your question. Good luck. – coffeemath Jun 13 '21 at 14:22
  • Practical simplex algorithms don't use artificial variables. They are truly artificial: only for introductory textbooks. Of course, they use slacks (aka logical variables). They stay in the model (well, they are implicit). – Erwin Kalvelagen Jun 15 '21 at 18:09

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