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bug in LinearProgramming
*To*: mathgroup at smc.vnet.net
*Subject*: [mg95487] bug in LinearProgramming
*From*: Veit Elser <ve10 at cornell.edu>
*Date*: Tue, 20 Jan 2009 05:44:23 -0500 (EST)
This is a re-post because the original did not draw any comments.
The data
c = {1, 1};
m = {{1, 0}, {1, -2}, {-1, 1}};
b = {{1, 0}, {0, 1}, {0, 1}};
lu = {{0, 1}, {0, 1}};
d = {Reals, Reals};
used in
LinearProgramming[c, m, b, lu, d]
corresponds to the problem
minimize x1+x2
subject to the constraints
x1 == 1, x1-2*x2 >= 0, -x1+x2 >= 0
with real variables in the ranges
0 <= x1 <= 1, 0 <= x2 <= 1
It's clear that this problem has no solution, and Mathematica
recognizes this fact.
But when the domain of x2 is changed to Integers, Mathematica returns
the "solution"
x1 == 1., x2 == 1
This violates the constraint x1-2*x2 >= 0.
**** earlier posting ****
Here is a simple linear programming problem:
c = {1, 1};
m = {{1, 0}, {1, -2}, {-1, 1}};
b = {{1, 0}, {0, 1}, {0, 1}};
lu = {{0, 1}, {0, 1}};
d = {Reals, Reals};
sol = LinearProgramming[c, m, b, lu, d]
Mathematica 6 returns:
LinearProgramming::"lpsnf" : "No solution can be found that
satisfies the constraints."
which is obviously correct. But if I change the domain of the second
variable,
d = {Reals, Integers};
then Mathematica gives the solution
sol = {1., 1}. The problem is that
m.sol = {1., -1., 0.}
violates the bound vector b (second component should be greater than 0).
Is there a bug, or am I getting the syntax wrong?
Veit Elser
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