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 >