Error in optim/constrOptim "initial value in 'vmmin' is not finite" - r

Question

My problem (and what I think could help to solve it) is explained until the line "FOR REPRODUCTION". After that I just posted my code, just in case reproducing might help to solve it.
I use optim and constrOptim.nl to solve an optimization problem with constraints within the function g (see below) I wrote.
I know that the initial values used below are not ideal, but I chose them
because they cause the problem I face in a shorter program. I use this program to calibrate model parameters to data and there this problem also occurs for better inital values, higher tolerances etc.
The Error
I call the function get_par I wrote with:
v<-c(0.12504710,0.09329359,0.06778733, 0.04883216, 0.04187344,0.02886261,0.02332951,0.02178576,0.02282214,0.02956336,0.03478598)
Ti=1/12
x<-log(cbind(0.8,0.85,0.9,0.95,0.975,1,1.025,1.05,1.1,1.15,1.2))
g(par2=c(-5,5),v=v,Ti=Ti,x=x)
Then I get
Error in optim: inital value 'vmmin' is not finite.
What I have observed so far
So I started to debug my code to find out where exactly this error occurs. The error occurs in the function g (see below) in the line ( with the values sigma=5,m=-5,y=(x-m)/sigma,vtilde=v/12)
#print(paste("vW: sigma: ",sigma,"mv:",mv))
argmin<-constrOptim.nl(par=c(3*sigma,sigma,mv/2),fn=f,hin.jac=hinv.jac,
hin=hinv,heq.jac=heqv.jac,heq=heqv,control.outerlist(trace=T),
control.optim=list(abstol=10^(-10)),y=y,vtilde=vtilde,sigma=sigma)
The Trace of the funciton constrOptim.nl displays
Outer iteration: 18
Min(hin): 1.026858e-19 Max(abs(heq)): 0
par: 10 9.99998 1.02686e-19
fval = 6399
for the last iteration. I guess that there is some sort of a numerical problem with 1.02686e-19 appearing in the last iteration.
I had a look into the function constrOptim.nl and albama (with debug() ), and the error exactly occurs in the line
theta.old <- theta
atemp <- optim(par = theta, fn = fun, gr = grad, control = control.optim,
method = "BFGS", hessian = TRUE, ...)
where theta=theta.old has the value
Browse[2]> theta.old
[1] 1.000002e+01 9.999985e+00 -3.349452e-20
Hence it has an entry that is just below zero (its absolute value is even smaller than machine accuracy, isn't it?).
When you look at the function fun you realize that it calls the function
R:
function (theta, theta.old, ...)
{
gi <- hin(theta, ...)
if (any(gi < 0))
return(NaN)
gi.old <- hin(theta.old, ...)
hjac <- hin.jac(theta.old, ...)
bar <- sum(gi.old * log(gi) - hjac %*% theta)
if (!is.finite(bar))
bar <- -Inf
fn(theta, ...) - mu * bar
}
hin(theta,...)=hinv(theta,...) returns a vector with a negative entry, thus this function returns NaN. I suppose that this should cause the error message: "Error in optim: inital value 'vmmin' is not finite". My question is now:
How can I fix that? I thought of forcing the program to terminate somehow when such small values occur, but I have not managed to do that yet. What do yo suggest?
Many thanks in advance,
FOR REPRODUCTION:
Here is my program:
The functions hinv, hinv.jac, heq and heq.jac are just for the constraints. The function where I optimize is g.
library(alabama)
library(dfoptim)
#function f, par = (c,d,atilde)
f<-function(par3,y,vtilde,sigma){
sum((par3[3]+par3[2]*y+par3[1]*sqrt(y^2+1)-vtilde)^2)
}
#Equality/Inequality constraints
heqv<-function(par3,y,vtilde,sigma){
J1<-matrix(1/2*cbind(sqrt(2),sqrt(2),-sqrt(2),sqrt(2)),nrow=2,ncol=2)
J2<-matrix(0,nrow=3,ncol=3)
J2[1:2,1:2]<-J1
J2[3,3]<-1
j<-J2%*%par3
j[2]-2*sqrt(2)*sigma
}
#Jacobian-matrix
hinv.jac<-function(par3,y,vtilde,sigma){
#J1, J2: Drehungen für die constraints
J1<-matrix(1/2*cbind(sqrt(2),sqrt(2),-sqrt(2),sqrt(2)),nrow=2,ncol=2)
J2<-matrix(0,nrow=3,ncol=3)
J2[1:2,1:2]<-J1
J2[3,3]<-1
hjac<-matrix(cbind(1,-1,0,0,0,0,0,0,0,0,1,-1),nrow=4)%*%J2
hjac
}
hinv<-function(par3,y,vtilde,sigma){
#J1, J2: Drehungen für die constraints
J1<-matrix(1/2*cbind(sqrt(2),sqrt(2),-sqrt(2),sqrt(2)),nrow=2,ncol=2)
J2<-matrix(0,nrow=3,ncol=3)
J2[1:2,1:2]<-J1
J2[3,3]<-1
j<-J2%*%par3
h<-rep(NA,4)
h[1]<- j[1]
h[2]<- sqrt(2)*2*sigma-j[1]
h[3]<-j[3]
h[4]<-max(vtilde)-j[3]
h
}
#Jacobian-matrix
heqv.jac<-function(par3,y,vtilde,sigma){
#J1, J2: Drehungen für die constraints
J1<-matrix(1/2*cbind(sqrt(2),sqrt(2),-sqrt(2),sqrt(2)),nrow=2,ncol=2)
J2<-matrix(0,nrow=3,ncol=3)
J2[1:2,1:2]<-J1
J2[3,3]<-1
cbind(J2[2,1],J2[2,2],0)
}
#function g input: par2= (m,sigma): optimization of function f
g<-function(par2,v,Ti,x){
#definition of parameters being used
m<-par2[1]
sigma<-par2[2]
y<-(x-m)/sigma #Transformation von x zu y gemäß paper
vtilde<-Ti*v
mv<-max(vtilde)
#print(paste("vW: sigma: ",sigma,"mv:",mv))
argmin<-constrOptim.nl(par=c(3*sigma,sigma,mv/2),fn=f,hin.jac=hinv.jac,hin=hinv,heq.jac=heqv.jac,heq=heqv,control.outer=list(trace=F),control.optim=list(abstol=10^(-10)),y=y,vtilde=vtilde,sigma=sigma)
argmin$par
}