[Coin-bcpdiscuss] Variable LB fixed to 1 by BCP

[Matteo Salani]

Laszlo Ladanyi wrote:
> Reduced cost fixing can happen both on lower and on upper bounds. If a
> variable is out of basis at its upper bound then if its reduced cost is very
> negative then it can be fixed to its upper bound. The argument is the same
> that you use when a variable is out of basis at its lower bound has high
> positive reduced cost. It's just that the latter situation (especially when
> the lower bound is 0) hapens a lot more frequently.
>   
Dear Laszlo, thanks a lot for your answer,

I still have some doubts: to me lower bound fixing as you explained 
makes sense when no more variable can be generated.
During the CG I have no guarantee that a new (better) variable could be 
generated and enter the formulation.

> To check that things a re OK get the reduced costs and the warmstart
> information (just use getWarmstart on the osi solver interface). The latter
> will give you the basis status information for everything. In there look up
> the status of your variable (watch out, it's a compressed array, there are 2
> bits per entry). If it's out of basis at its upper bound and the reduced cost
> of the var is very negative then you are OK.
>   
I did this check:
I saved the LP of an iteration where the variable was already fixed at 
the upper bound. I solved the linear relaxation and obtained a feasible 
optimal value Xf. I just removed the bound on one variable and obtained 
a feasible optimal value Xr << Xf. We're still talking about linear 
relaxations (no branching made so far). Is it enough to claim that the 
lb fixing was wrong?

Matteo

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