Problem with optimization using solnp in R - r

Question

I'm having some issues with the following problem:
I want to maximize the function U with respect to the constraint B using solnp()
I've defined the U function as:
U = function(x){
#P is a vector of parameters
#X is a vector of variables
-P[1]*(x[1]^P[2])*(x[2]^P[3])
}
And the function B as follows:
B = function(x){
#M is a vector of parameters
#X is a vector of variables
#The constant M[3] is an argument of CCM
-M[1]*x[1]-M[2]*x[2]
}
Then I've defined the optimizer function this way as a cover of solnp():
CCM = function(P,M){
solnp(c(0,0), #starting values (random - obviously need to be positive and sum to 15)
U, #function to optimise
eqfun=B, #equality function
eqB=-M[3], #the equality constraint
LB=c(0,0), #lower bound for parameters i.e. greater than zero
UB=c(10000,10000)) #upper bound for parameters (I just chose 10000 randomly)
}
I've written a optimize function to be able to choose different parameters for this problem.
The issue here is that when I run the CCM function is does not seem to be maximizing (gives me (0,0) as solution), solnp() minimizes by default, so I've changed the sign of U and B due to that.
By the way, I'm trying to program a Consumer Choice model.
Edit:
Test run with the values in the OP's comment.
P <- c(2,0.1,0.9)
M <- c(1,2,15)
CCM(P, M)
#
#solnp-->The linearized problem has no feasible
#solnp-->solution. The problem may not be feasible.
#
#Iter: 1 fn: 0 Pars: 0 0
#solnp--> Solution not reliable....Problem Inverting Hessian.
#$pars
#[1] 0 0
#
#$convergence
#[1] 2
#
#$values
#[1] 0 0
#
#$lagrange
#[1] 0
#
#$hessian
# [,1] [,2]
#[1,] 1 0
#[2,] 0 1
#
#$ineqx0
#NULL
#
#$nfuneval
#[1] 7
#
#$outer.iter
#[1] 1
#
#$elapsed
#Time difference of 0.6487024 secs
#
#$vscale
#[1] 1.0e-08 1.5e+01 1.0e+00 1.0e+00
#
CCM(P, M)$convergence
#
#solnp-->The linearized problem has no feasible
#solnp-->solution. The problem may not be feasible.
#
#Iter: 1 fn: 0 Pars: 0 0
#solnp--> Solution not reliable....Problem Inverting Hessian.
#[1] 2

Answer 1

You can consider the following approach :
U <- function(val_x, val_P)
{
val_P[1] * (val_x[1] ^ val_P[2]) * (val_x[2] ^ val_P[3])
}
B <- function(val_x, val_M)
{
val_M[1] * val_x[1] - val_M[2] * val_x[2]
}
fn_Opt <- function(val_x, val_P, val_M)
{
val <- (B(val_x, val_M) - M[3]) ^ 2 + U(val_x, val_P)
if(is.na(val) | is.nan(val) | is.infinite(val))
{
return(10 ^ 30)
}else
{
return(val)
}
}
library(DEoptim)
P <- c(2, 0.1, 0.9)
M <- c(1, 2, 15)
obj_DEoptim <- DEoptim(fn = fn_Opt, lower = c(0,0), upper = c(10000,10000),
control = list(itermax = 1000), val_P = P, val_M = M)
obj_DEoptim$optim$bestmem
par1 par2
1.500000e+01 5.661556e-134
B(obj_DEoptim$optim$bestmem, M)
par1
15
U(obj_DEoptim$optim$bestmem, P)
par1
3.135316e-120