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<div class="moz-cite-prefix">On 9/23/2013 9:04 AM, William H. Patton
wrote:<br>
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<blockquote cite="mid:52404A6C.6020604@comcast.net" type="cite">
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Why do you think the values of the solution vars are guaranteed ?
Only the objective sum is guaranteed.<br>
I think you mark column 28 suspect. I think this is variable
named X20.<br>
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.<br>
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.<br>
Model size: 28 constraints, 32 variables, 84
non-zeros.<br>
\* Objective function *\<br>
Minimize<br>
COST: -0.4 X02 -0.32 X14 -0.6 X23 -0.48 X36 +10 X39<br>
<br>
For instance I can add the bound X28 <= 200 and still get
the same objective only now X28 = 200.<br>
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.<br>
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<br>
is needed if you care to find them.<br>
<br>
William<br>
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