AUGLAG roundoff error returns initial condition.

[lawbaker]

Thanks for maintaining nloptr!

I've identified a bug where the Augmented Lagrangian does not return the most recent solution when encountering a roundoff error (status code -4). Instead it returns the initial condition.

The code below demonstrates that when BOBYQA is called outside of AUGLAG, it correctly returns the most recent solution before the roundoff error. When the same function is used inside AUGLAG, then it returns the correct status code (-4), but the wrong solution, defaulting to the initial condition.

library(nloptr)

optim_function <- function(x){
  util <- log(x) + log(1e10-x)
  return(-util)
}

optim <- nloptr(x0 = 3,
               eval_f = optim_function,
               lb = 1e-8,
               ub = 1e10 - 1e-8,
               opts = list(algorithm = "NLOPT_LN_BOBYQA",
                           xtol_abs = 1e-30,
                           xtol_rel = 0,
                           ftol_rel = 0,
                           ftol_abs = 1e-30,
                           maxeval = 100000))

optim_aug <- nloptr(x0 = 3,
                eval_g_ineq = function(x){-x},
                eval_f = optim_function,
                lb = 1e-8,
                ub = 1e10 - 1e-8,
                opts = list(algorithm = "NLOPT_LN_AUGLAG",
                            xtol_abs = 1e-30,
                            xtol_rel = 0,
                            ftol_rel = 0,
                            ftol_abs = 1e-30,
                            maxeval = 100000,
                            local_opts = list(algorithm = "NLOPT_LN_BOBYQA",
                                              xtol_abs = 1e-30,
                                              xtol_rel = 0,
                                              ftol_rel = 0,
                                              ftol_abs = 1e-30,
                                              maxeval = 100000)))


optim$status
optim$solution

optim_aug$status
optim_aug$solution

This returns

> optim$status
[1] -4
> optim$solution
[1] 202472257

> optim_aug$status
[1] -4
> optim_aug$solution
[1] 3

I am running

nloptr_2.0.3

R version 4.4.0 (2024-04-24 ucrt)
Platform: x86_64-w64-mingw32/x64
Running under: Windows 10 x64 (build 19045)

[astamm]

Thanks for reporting this!

I was able to reproduce the issue locally.
Note that I commented out eval_g_ineq = function(x){-x}, to make the two calls match.

I will investigate this but I believe it is an issue that should be filed in the original nlopt repo.

[lawbaker]

Thanks! I wasn't sure if this was a general nlopt problem or a nloptr-specific issue.

[astamm]

The objective function value at the optimum is different as well (it is -42.13151 for optim object with minimum returned at 202472257 while it is +Inf for the optim_aug object with minimum returned at 3).

The internal code of nloptr only calls internally nlopt_optimize() with optimizer options properly set as given by the user. So I suppose this is an nlopt issue rather than an nloptr issue.

We should try to reproduce this issue outside nloptr with only nlopt. Could you do that? If not, let me know and I'll do it.