problem with optim()

First, thank you for ur response...
Actually I didn't write the entire code ...X, Y and p_tilde are of
course?all defined?at the beginning of my?code.

Normally?the optimal values that?I get should?let me?create a model for
prediction. However?the model currently obtained is not good at all....

And?I think that the fact? it gives me the exactly same values if?I
change?the function to maximize?shows that there's a problem in my code....

Date: Thu, 19 May 2011 09:29:02 -0400
Subject: Re: [R] problem with optim()
From: biomathjdaily at gmail.com
To: wolley.chirine at hotmail.com
CC: r-help at r-project.org

What do you mean when you say "wrong results"? What do you expect for
the output? Your code doesn't work for me because it references X in
places and X is not defined.

Have you tested your functions to make sure they return reasonable values?

On Thu, May 19, 2011 at 9:17 AM, chirine wolley
<wolley.chirine at hotmail.com> wrote:

Dear R-users,

I would like to maximize the function g above which depends on 4
parameters (2 vectors, 1 real number, and 1 matrix) ?using optim() and BFGS
method. Here is my code:

# fonction to maximize

g=function(x)
{
x1 = x[1:ncol(X)]
x2 = x[(ncol(X)+1)]
x3 =
matrix(x[(ncol(X)+2):(ncol(X)+1+ncol(X)*ncol(Y))],nrow=ncol(X),ncol=ncol(Y))
x4 = x[(ncol(X)+1+ncol(X)*ncol(Y)+1):length(x)]
res1=rep(0,nrow(X))
res2=matrix(0,nrow=nrow(X),ncol=ncol(Y))
log.res2=matrix(0,nrow=nrow(X),ncol=ncol(Y))
res2.b=rep(0,nrow(X))
res3 = rep(0,nrow(X))
res3.b = rep(0,nrow(X))
for (i in 1:nrow(X))
{
res1[i]=1/(1+exp(-t(x1)%*%X[i,]-x2))
for (t in 1:ncol(Y))
{
res2[i,t] =
((1-(1+exp(-t(x3[,t])%*%X[i,]-x4[t]))^(-1))^(abs(Y[i,t]-Yb[i])))*(((1+exp(-t(x3[,t])%*%X[i,]-x4[t]))^(-1))^(1-abs(Y[i,t]-Yb[i])))
log.res2[i,t]=log(res2[i,t])
res2.b[i]=res2.b[i]+log.res2[i,t]
}
res3[i] = p_tilde[i]*log(res1[i])
res3.b[i] = p_tilde[i]*(res2.b[i])
}
-(ncol(Y)*sum(res3)+sum(res3.b))

}

##### Gradiants:

gr=function(x)
{
x1 = x[1:ncol(X)]
x2 = x[(ncol(X)+1)]
x3 =
matrix(x[(ncol(X)+2):(ncol(X)+1+ncol(X)*ncol(Y))],nrow=ncol(X),ncol=ncol(Y))
x4 = x[(ncol(X)+1+ncol(X)*ncol(Y)+1):length(x)]
gr1 = rep(0,ncol(X))
gr4 = rep(0,ncol(Y))
gr3 = matrix(0,nrow=ncol(X),ncol=ncol(Y))
gr1.b = matrix(0,nrow=nrow(X),ncol=ncol(X))
gr2.b = rep(0,nrow(X))
eta = matrix(0,nrow=nrow(X),ncol=ncol(Y))
d.eta.3 = array(0,dim=c(nrow(X),ncol(X),ncol(Y)))
d.eta.4 = matrix(0,nrow=nrow(X),ncol=ncol(Y))
gr3.b1 = array(0,dim=c(nrow(X),ncol(X),ncol(Y)))
gr4.b1 = matrix(0,nrow=nrow(X),ncol=ncol(Y))

#Gradiant of alpha and beta

for (i in 1:nrow(X))
{
gr1.b[i,] =
(2*p_tilde[i]-1)*((exp(-t(x1)%*%X[i,]-x2)*X[i,])/(1+exp(-t(x1)%*%X[i,]-x2))^2)
gr2.b[i] =
(2*p_tilde[i]-1)*((exp(-t(x1)%*%X[i,]-x2))/(1+exp(-t(x1)%*%X[i,]-x2))^2)
}
for (j in 1:ncol(X))
{
gr1[j] = sum(gr1.b[,j])
}
gr2 = sum(gr2.b)


#Gradiant de w et gamma
for (i in 1:nrow(X))
{
for (t in 1:ncol(Y))
{
eta[i,t] = 1/(1+exp(-t(x3[,t])%*%X[i,]-x4[t]))
d.eta.3[i,,t] = eta[i,t]*(1-eta[i,t])*X[i,]
d.eta.4[i,t] = eta[i,t]*(1-eta[i,t])
gr3.b1[i,,t] =
p_tilde[i]*((-abs(Y[i,t]-Yb[i]))*(1-eta[i,t])^(-1)+(1-abs(Y[i,t]-Yb[i]))*
(eta[i,t])^(-1))*d.eta.3[i,,t]
gr4.b1[i,t] =
p_tilde[i]*((-abs(Y[i,t]-Yb[i]))*(1-eta[i,t])^(-1)+(1-abs(Y[i,t]-Yb[i]))*
(eta[i,t])^(-1))*d.eta.4[i,t]
}
}
for (t in 1:ncol(Y))
{
for (j in 1:ncol(X))
{
gr3[j,t] = sum(gr3.b1[,j,t])
}
gr4[t] = sum(gr4.b1[,t])
}
c(-gr1,-gr2,-gr3,-gr4)
}

opt = optim(c(alpha[,c+1],beta[c+1],w,gamma),g,gr,method="BFGS")

The problem is that it gives me wrong results, and I have noticed that
if I change my function to maximize (for example if, instead of
-(ncol(Y)*sum(res3)+sum(res3.b)), I try to maximise -(ncol(Y)*sum(res3)), it
gives me the exactly same results...which is not possible!
So maybe I am using optim() in a wrong way...Does someone have an idea
what could be wrong in my code ?

Thank you very much in advance
? ? ? ?[[alternative HTML version deleted]]

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