[Clp] Possible different treatment for Bounds and Constraints Section

[John J Forrest]

Are you sure your problem is really feasible?

There are differences in how bounds and constraints are treated.  Take the
following example (with default infeasibility tolerance of 1.0e-7).

x is free and we have three constraints

x==0.0
x>=0.6e-7
x<=-0.6e-7

Now x can pivot into basis on first constraint and the slacks on other two
constraints can take values of -0.6e-7 which while infeasible is within
tolerance.

If x<= -0.6e-7 is converted into a bound then IF x is basic on first
constraint then both x and a slack are infeasible but within bounds.  BUT
if x starts out non-basic i.e at -0.6e-7 then it is never allowed to
increase to come into basis and so slack will have infeasibility of 1.2e-7.

Finally if both constraints are made into bounds then the problem will be
immediately declared to be infeasible as the lower bound on x is greater
than the upper bound.

John Forrest


                                                                                                                 
  From:       Emrah Tanriverdi <emrahtanriverdi at yahoo.com>                                                       
                                                                                                                 
  To:         clp at list.coin-or.org                                                                               
                                                                                                                 
  Date:       05/19/2009 11:02 AM                                                                                
                                                                                                                 
  Subject:    [Clp] Possible different treatment for Bounds and Constraints     Section                          
                                                                                                                 





  I was trying to solve a problem with CLP, and I encountered a Primal
Infeasibility with tolerance of 1.0e-6. After a cumbersome debugging
procedure, I found that it is because of a Variable in Bound Section (that
it shouldn't cause). So, I changed the place of the Upper Bound of the
Variable from Bound Section to Constraint Section, and then CLP was able to
solve it to optimality. With same upper bound in Bounds Section, CLP
complaint infeasibility, whereas it solved to optimality when it is in
Constraint Section.
    It seems, Constraint Section and Bound Section has different rounding
or treatment or may be it was because of perturbation we are using. Can
someone explain what is going on and what may be the cause?
    Thanks,
    Emrah
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