Optimization in R Non linear programming

[KafeelI]

Hello

I am trying to solve a simple non linear programming problem using R.

#Maximize profit p
x1=14
x2<=20
x3>=5000
p=x2*x3-x1*x3

Below is the R code I have tried, let me know where I am going wrong.

library(ROI)
library(ROI.plugin.nloptr)
prob<-OP(objective=F_objective(F=function(x){x[2]*x[3]-x[1]*x[3]},n=3),
         constraints=F_constraint(F=function(x){c(x[1],x[2],x[3])}, dir=c("<=","<=",">="),rhs=c(14,20,5000),J=function(x)c(1,0,0,0,1,0,0,0,1)),maximum=TRUE)

ROI_solve(prob,solver="nloptr",start=c(10,10,4000))

[rcgayle]

Did you really mean the first constraint to read 'x1=14'? Because, if that is the case, it's not necessary to include x1 in the objective function; you could simply replace it with 14 and do the resulting contrained optimization in R^2 (over x2 and x3).

Also, I do not see any of the contraints you've outlined in the original problem appearing anywhere in the constraint specification in your code. Mind you, I've never used the package ROI.

[KafeelI]

Okay. So I have changed the objective function as below.

x1<=20
x2>=5000
p=x1*x2-14*x2

Any function or package which you can think of, using which I can optimize non linear objective function with linear constrains.

Thanks for your reply.

[rcgayle]

Yes, well there's another problem which didn't occur to me earlier. The objective function you've given has neither a maximum nor a minimum on the region described by the constraints.

To wit: Let x1=20 and let x2 go to positive infinity. Then p likewise grows without bound. On the other hand, with y=5000, as x1 goes to negative infinity p also goes to negative infinity. So it would be pointless to employ any method to try to optimize. In general you need a closed and bounded (compact) region and an objective function continuous on that region to be sure that both absolute extrema exist.

As to your other question, I am not familiar with any R pachages for numerical optimization but doubtless there are many.

[KafeelI]

Oh Yes, thank you.

There are multiple packages I came across now.