# [R] Penalty function constrained optimization

hayduke cusackc at onid.orst.edu
Tue Oct 16 20:06:42 CEST 2012

```Hi All,
I am trying to use optim() to minimize a function with a penalty function
term. This is a simple model bioeconomic model of a fishery. The penalty
function constrains the amount of effort (f) at 9. This works fine. The code
is:
**********
nfleets<-2
M<-1
M<-array(M,dim=c(nfleets))
N<-1000
cost<-c(30,30)
cost<-array(cost,dim=c(nfleets))
Price<-2
Price<-array(Price,dim=c(nfleets))
q<-array(0.1,dim=c(nfleets))
f<-1
f<-array(f,dim=c(nfleets))
f1<-f[1]
f2<-f[2]
init.eff<-array(8,dim=c(nfleets))
OF<-c(q*f)
F<- sum(q*f)
Z<-M+F
Catch<-array(0,dim=c(nfleets))

obj<-function(f){
F <- q*f
Z <- M+sum(F)
S <- exp(-Z)
Catch<- N*F/Z*(1-S)
Tot.Catch <- sum(Catch)
NR<-array(0,dim=c(nfleets))
NR<-Price*Catch - f*cost
d.NR<-array(0,dim=c(nfleets))
d.NR<- N*q/Z*(1-S-F/Z+F/Z*S+F*S)*Price-cost +1000*(max(0,f-9))^2
return(sum(d.NR*d.NR))}
zero.bnd <-  rep.int(0, length(f))
opt.eff  <- optim( init.eff, obj, method="L-BFGS-B", lower=zero.bnd )
***

However, now I am trying to add another dimension to the problem: areas.
Does anybody have any suggestions regarding how to implement the penalty
function so it works over all areas? i.e. that the sum of each fleet's
effort is 9 across all areas?
The code with areas is below. In the obj function, the ??? denote the start
of the penalty function and the place where I need help....
***
nfleets<-2
nareas<-2
M<-1
M<-array(M,dim=c(nfleets,nareas))
N<-1000
cost<-c(30,30)
cost<-array(cost,dim=c(nfleets,nareas))
Price<-2
Price<-array(Price,dim=c(nfleets,nareas))
q<-array(0.1,dim=c(nfleets,nareas))
f<-1
f<-array(f,dim=c(nfleets,nareas))
init.eff<-array(3,dim=c(nfleets,nareas))
OF<-array(c(q*f), dim=c(nfleets, nareas))
F<- sum(q*f)
Z<-M+F
Catch<-array(0,dim=c(nfleets, nareas))

obj<-function(f){
F <- q*f
Z <- M+sum(F)
S <- exp(-Z)
Catch<- N*F/Z*(1-S)
Tot.Catch <- sum(Catch)
NR<-array(0,dim=c(nfleets,nareas))
NR<-Price*Catch - f*cost
d.NR<-array(0,dim=c(nfleets,nareas))
d.NR<- N*q/Z*(1-S-F/Z+F/Z*S+F*S)*Price-cost +???????1000*sum(max(0,(f-9))^2
return(sum(d.NR*d.NR))}

zero.bnd <-  rep.int(0, length(f))
opt.eff  <- optim( init.eff, obj, method="Nelder-Mead" )

Thanks very much!

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