       Re: bug in LinearProgramming

• To: mathgroup at smc.vnet.net
• Subject: [mg95622] Re: bug in LinearProgramming
• From: dh <dh at metrohm.com>
• Date: Fri, 23 Jan 2009 05:05:43 -0500 (EST)
• References: <gl49u2\$g8i\$1@smc.vnet.net>

```
Hi Veit,

I think this is simply a bug with the recognition of conditions. In your

case, the second condition is ignored. If you change b to: {{1, 0}, {0,

0}, {0, 1}} the third condition is ignored. Please send this to Wolfram.

Daniel

Veit Elser wrote:

> 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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