[Clp] Questions about CLP (which I couldn't find in the FAQ, possibly because they're super-outdated)

[William H. Patton]

On 9/23/2013 9:04 AM, William H. Patton wrote:
> Why do you think the values of the solution vars are guaranteed ? Only 
> the objective sum is guaranteed.
> I think you  mark column 28 suspect.  I think this is variable named X20.
> lp_solve tells me X20 =  366.4378...  This seems to agree with CLP  
> where Simpo seems to have exact 0.0,  Barrier has perhaps 106 or 186 I 
> cannot quit read the image.
> Now X20 does not appear in the objective  so perhaps can assume many 
> values without changing the objective.  The matrix is not square non 
> singular so unique inverses are not guaranteed.
> Model size:       28 constraints,      32 variables,           84 
> non-zeros.
> \* Objective function *\
> Minimize
>  COST: -0.4 X02 -0.32 X14 -0.6 X23 -0.48 X36 +10 X39
>
> For instance I can add the bound    X28 <= 200   and  still get the 
> same objective    only now X28 = 200.
>   Equally I can set X28 = 0 without affecting the solution. Linear 
> programming only tries to guarantee a corner vertexx is found which 
> minimizes the objective.
> In particular it quits when there is no better corner. There may still 
> be other equally valid solutions at other corners. These can be quite 
> hard to enumerate. Essentially a depth first search
> is needed if you care to find them.
>
> William

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