R: Error in is.nloptr(ret) : objective in x0 returns NA

Question

I am trying to use the nloptr package to find the optimal x value that maximized the non-linear function F=b0+b1*x+b2*x^2+b3*x^3.

I am using the following code with appl

Answer 1

You should NOT be passing rows of "Regression" using apply if you are also intending to access items inside the function. There's also going to be a problem when apply coerces Regression to a single type. It will be character rather than numeric. Instead, it should be:

library(nloptr)
F <- function(x,b0,b1,b2,b3){return(b0+b1*x+b2*x^2+b3*x^3)}
Optimal <- apply(Regression[-1],     #removes first column
                                 1, function(i){   # i-variable gets values
                  nloptr( x0 <- c(0)
                         ,eval_f <- F
                         ,eval_g_ineq = NULL
                         ,eval_g_eq = NULL
                         ,eval_grad_f = NULL
                         ,eval_jac_g_ineq = NULL
                         ,eval_jac_g_eq = NULL
                         ,lb <- c(-Inf)
                         ,ub <- c(Inf)
                         ,opts <- list( "algorithm" = "NLOPT_LD_AUGLAG",
                                        "xtol_rel" = 1.0e-7,
                                        "maxeval" = 1000)
                         ,b0=i[1]
                         ,b1=i[2]
                         ,b2=i[3]
                         ,b3=i[4])})

Tested with your "Regression"-object. (I have concerns about whether there will be a minimum or a maximum when attempting to work with a cubic polynomial.) Unfortunately you have chosen parameters that are inconsistent:

Error in is.nloptr(ret) : 
  A gradient for the objective function is needed by algorithm NLOPT_LD_AUGLAG 
but was not supplied.

It should be possible to calculate a gradient of a polynomial without too much difficulty, though.

After constructing a gradient function I now get:

grad_fun <- function(x,b0,b1,b2,b3) { b1 + x*b2/3 +x^2*b3/3 }
> F <- function(x, b0,b1,b2,b3){return(b0+b1*x+b2*x^2+b3*x^3)}
> Optimal <- apply(Regression[-1],     
+                                  1, function(i){   
+                   nloptr( x0 <- c(0)
+                          ,eval_f <- F
+                          ,eval_g_ineq = NULL
+                          ,eval_g_eq = NULL
+                          ,eval_grad_f = grad_fun
+                          ,eval_jac_g_ineq = NULL
+                          ,eval_jac_g_eq = NULL
+                          ,lb <- c(-Inf)
+                          ,ub <- c(Inf)
+                          ,opts <- list( "algorithm" = "NLOPT_LD_AUGLAG",
+                                         "xtol_rel" = 1.0e-7,
+                                         "maxeval" = 1000)
+                          ,b0=i[1]
+                          ,b1=i[2]
+                          ,b2=i[3]
+                          ,b3=i[4])})
Error in is.nloptr(ret) : 
  The algorithm NLOPT_LD_AUGLAG needs a local optimizer; specify an algorithm and termination condition in local_opts

Seemed to me that I've gotten you past several hurdles, so this is not yet really an answer but it seems useful and was far too long for a comment.

Edit; Further experiments with changing the algorithm to "algorithm" = "NLOPT_LD_LBFGS" gets the code to run without error but as far as I can see the 4 runs all returned list with $ message : chr "NLOPT_FAILURE: Generic failure code.". My guess is that optimizing cubic polynomials will generally fail without constraints and I see none in your problem specification.