R help - Dec 2009 - Solve linear program without objective function

Dear R-users,

i try to solve to following linear programm in R

0 * x_1 + 2/3 * x_2 + 1/3 * x_3 + 1/3 * x_4 = 0.3
x_1 + x_2 + x_3 + x_4 = 1
x_1, x_2, x_3, x_4 > 0,
x_1, x_2, x_3, x_4 < 1

as you can see i have no objective function here besides that i use the 
following code.


library(lpSolve)

f.obj<-c(1,1,1,1)
f.con<-matrix(c(0,2/3,1/3,1/3,
                1,1,1,1,
                1,0,0,0,
                0,1,0,0,
                0,0,1,0,
                0,0,0,1),nrow=6,byrow=TRUE)
f.dir <- c("=", "=", ">", ">",
">", ">")
f.rhs <- c(0.3, 1, 0, 0, 0, 0)

lp ("max", f.obj, f.con, f.dir, f.rhs)$solution


the problem is, the condition x_1, x_2, x_3, x_4 > 0 is not fulfilled.

Any advice would be very helpful.

best regards

Andreas

Andreas Wittmann <andreas_wittmann <at> gmx.de> writes:
> 
> Dear R-users,
> 
> i try to solve to following linear programm in R
> 
> 0 * x_1 + 2/3 * x_2 + 1/3 * x_3 + 1/3 * x_4 = 0.3
> x_1 + x_2 + x_3 + x_4 = 1
> x_1, x_2, x_3, x_4 > 0,
> x_1, x_2, x_3, x_4 < 1
> 
> as you can see i have no objective function here besides that i use the 
> following code.
> 
> library(lpSolve)
> 
> f.obj<-c(1,1,1,1)
> f.con<-matrix(c(0,2/3,1/3,1/3,
>                 1,1,1,1,
>                 1,0,0,0,
>                 0,1,0,0,
>                 0,0,1,0,
>                 0,0,0,1),nrow=6,byrow=TRUE)
> f.dir <- c("=", "=", ">",
">", ">", ">")
> f.rhs <- c(0.3, 1, 0, 0, 0, 0)
> 
> lp ("max", f.obj, f.con, f.dir, f.rhs)$solution
> 
> the problem is, the condition x_1, x_2, x_3, x_4 > 0 is not fulfilled.
With strict inequalities x_i > 0 your problem will not have a solution. That
is
why in linear programming strict inequalities are replaced with non-strict
inequalities, or as the lp_solve manual says:

    "The inequalities can be <=, >= or      Because all numbers are
real values,
     <= is the same as < and >= is the same as > ." 

Try x_i >= eps > 0 with some eps appropriate for your problem.

Hans Werner
> Any advice would be very helpful.
> 
> best regards
> 
> Andreas
> 
>

Andreas,
 
I don't know what it is exactly that you want to do, but perhaps you can try
using limSolve,
which solves for the equations Ex>=F, Gx>=H. In the code below, lsei
calculates the least squares solution (min sum(x^2)), xranges estimates the
range of your variables, and xsample takes a random sample of solutions.
 
f.con<-matrix(c(0,2/3,1/3,1/3,
                1,1,1,1,
                1,0,0,0,
                0,1,0,0,
                0,0,1,0,
                0,0,0,1),nrow=6,byrow=TRUE)
f.rhs <- c(0.3, 1, 0, 0, 0, 0)
 
 
E<- f.con[1:2,]
G<- f.con[-(1:2),]
F<- f.rhs[1:2]
H<-f.rhs[-(1:2)]
 
require(limSolve)
 
lsei(E=E,F=F,G=G,H=H)
xranges(E=E,F=F,G=G,H=H)
xs <- xsample(E=E,F=F,G=G,H=H)
pairs(xs$X)

 
Hope this helps,
 
Karline

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