R help - Dec 2008 - Simplex function in R

I have a set of linear equations and would like to find any feasible solution. 
A simplex solution works in Case 1 below, but not in Case 2.  I would be
grateful for any help.

Case 1: Find any feasible solution for the set of linear equations:
  a  +   b   +   c  = 5
  a  +   b  +  0c  = 4
0a +   b   +   c  =  4

Solution - a feasible (and unique) solution is a=1, b=3, c=1.

The following R code returns a feasible solution:
A3M = matrix(c(1,1,0,1,1,1,1,0,1),nrow=3)
b3M = matrix(c(5,4,4),ncol=1)
A1M = matrix(c(1,0,0,0,1,0,0,0,1),nrow=3)
b1M = matrix(c(10,10,10),ncol=1)
AM = matrix(c(1,1,1),nrow=1)
simplex(a = AM, A1 = A1M, b1 = b1M, A2 = NULL, b2 = NULL, A3 = A3M, b3 = b3M,
maxi = TRUE)


Case 2: Find any feasible solution for the set of linear equations
   a +   b   +   c  = 5
   a + 0b  +   c  = 2
0a +   b   + 0c  = 3

Solution - one feasible solution of many is a=1, b=3, c=1.  There are infinite
possible solutions in Case 2.

However, the following R code fails to return any feasible solution:
A3M = matrix(c(1,1,0,1,0,1,1,1,0),nrow=3)
b3M = matrix(c(5,2,3),ncol=1)
A1M = matrix(c(1,0,0,0,1,0,0,0,1),nrow=3)
b1M = matrix(c(10,10,10),ncol=1)
AM = matrix(c(1,1,1),nrow=1)
simplex(a = AM, A1 = A1M, b1 = b1M, A2 = NULL, b2 = NULL, A3 = A3M, b3 = b3M,
maxi = TRUE)

The code returns the error:
Error in A.out[, basic] <- iden(M) : subscript out of bounds

Am I using the Simplex function incorrectly?  There may be a better way to
approach the problem of finding a feasible solution.

Cheers,
Chris.

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Hi,
in the first example, your feasible set is just one point (the one
that fulfills the 3 equations) and thus there is only this one point
which can maximize the objective function. In the second case, the
feasible set is a line. But the simplex algorithm tries to find an
optimizing value of the objective on a convex polyhedron. So the
simplex function may be inappropriate to find all feasible solutions.

HTH
Armin

Try the pseudo inverse:

m <- rbind(c(1, 1, 1), c(1, 0, 1), c(0, 1, 0))
b <- c(5, 2, 3)

library(MASS)
ginv(m) %*% b


On Thu, Dec 11, 2008 at 2:20 AM, Chris Line <chris.line at tibra.com.au>
wrote:
> I have a set of linear equations and would like to find any feasible
solution.  A simplex solution works in Case 1 below, but not in Case 2.  I would
be grateful for any help.
>
> Case 1: Find any feasible solution for the set of linear equations:
>  a  +   b   +   c  = 5
>  a  +   b  +  0c  = 4
> 0a +   b   +   c  =  4
>
> Solution - a feasible (and unique) solution is a=1, b=3, c=1.
>
> The following R code returns a feasible solution:
> A3M = matrix(c(1,1,0,1,1,1,1,0,1),nrow=3)
> b3M = matrix(c(5,4,4),ncol=1)
> A1M = matrix(c(1,0,0,0,1,0,0,0,1),nrow=3)
> b1M = matrix(c(10,10,10),ncol=1)
> AM = matrix(c(1,1,1),nrow=1)
> simplex(a = AM, A1 = A1M, b1 = b1M, A2 = NULL, b2 = NULL, A3 = A3M, b3 =
b3M, maxi = TRUE)
>
>
> Case 2: Find any feasible solution for the set of linear equations
>   a +   b   +   c  = 5
>   a + 0b  +   c  = 2
> 0a +   b   + 0c  = 3
>
> Solution - one feasible solution of many is a=1, b=3, c=1.  There are
infinite possible solutions in Case 2.
>
> However, the following R code fails to return any feasible solution:
> A3M = matrix(c(1,1,0,1,0,1,1,1,0),nrow=3)
> b3M = matrix(c(5,2,3),ncol=1)
> A1M = matrix(c(1,0,0,0,1,0,0,0,1),nrow=3)
> b1M = matrix(c(10,10,10),ncol=1)
> AM = matrix(c(1,1,1),nrow=1)
> simplex(a = AM, A1 = A1M, b1 = b1M, A2 = NULL, b2 = NULL, A3 = A3M, b3 =
b3M, maxi = TRUE)
>
> The code returns the error:
> Error in A.out[, basic] <- iden(M) : subscript out of bounds
>
> Am I using the Simplex function incorrectly?  There may be a better way to
approach the problem of finding a feasible solution.
>
> Cheers,
> Chris.
>
> The contents of this email including any attachments are confidential. If
you have received this email in error, please advise the sender by return email
and delete this email. Any unauthorised use of the contents of the email is
prohibited and you must not disseminate, copy or distribute the message or use
the information contained in the email or its attachments in any way.
>
> The views or opinions expressed are the author's own and may not
reflect the views or opinions of Tibra. Tibra does not guarantee the integrity
of any emails or attached files. E-mails may be interfered with, may contain
computer viruses or other defects. Under no circumstances do we accept liability
for any loss or damage which may result from your receipt of this message or any
attachments.
>
>        [[alternative HTML version deleted]]
>
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