Originally posted by: vdesai

Hi all,
I have a general question regarding the barrier method implementation in cplex. I am interested in using barrier method to solve an LP. Does the barrier method (that cplex implements) maintain a primal feasible solution and dual feasible solution? From the log file it does not seem like that is the case. Is there any way around this? Any pointers/suggestions are welcome. Thanks.

Best,
Vijay
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Originally posted by: SystemAdmin

The barrier method is a primal-dual method. That means, it simultaneously drives the primal and dual solution to feasibility. As a consequence, throughout the algorithm both vectors will usually be infeasible, and you reach primal and dual feasibility only at the very end.
I am not sure, but I think that this is true for barrier algorithms in general, not only the one implemented in CPLEX.
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Originally posted by: vdesai

There are some interior point methods which maintain a primal and dual feasible point at all iterations. E.g. is central path method as described here
http://www.ee.ucla.edu/ee236a/lectures/barrier.pdf. I think the method that cplex implements are much better in practice, however they do not maintain a primal and dual feasible solution at all iterations.
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