Solved – L-BFGS-B converging in iteration 0 in R

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I am trying to fit an F distribution to a given set using optim's L-BFGS-B method. For some reason, it is always converging at iteration 0, which obviously doesn't approximate the parameters I am looking for.

For reproduction purposes,

# A sample x ~ F(5, 8) with 5,000 observations. x <- rf(50000, 5, 8)  # Sample density. f <- density(x, from=min(x), to=max(x))  # Error function (root mean squared error) to be minimized. # Noteworthy F's degrees of freedom are rounded since they # are required to be integers. rmse <- function(params) {   sqrt(sum((df(f$x, round(params[1]), round(params[2])) - f$y)^2)) }  # L-BFGS-B optimization. o <- optim(c(50, 50),              # Initial parameters.            rmse,            lower=c(0, 0),          # F's degrees of freedom's domain            upper=c(2^16, 2^16),    # is [0,Inf).            method='L-BFGS-B',            control=list(trace=3))  print(o)

Here we should expect o$par $approx (5, 8)$ to correspond with our x definition. Instead, the optimization does not take place and returns the initial parameters, $(50, 50)$, claiming

 $message  [1] "CONVERGENCE: NORM OF PROJECTED GRADIENT <= PGTOL"

Any hint towards a successful optimization?

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Best Answer

The issue is with the round() function as it allows infinite optimal solutions. That is, $(5.1,8.1)$ is optimal and so is $(4.9,7.9)$. Getting rid of the round() function works.

    # A sample x ~ F(5, 8) with 5,000 observations. x <- rf(50000, 5, 8)  # Sample density. f <- density(x, from=min(x), to=max(x))  # Error function (root mean squared error) to be minimized. # Noteworthy F's degrees of freedom are rounded since they # are required to be integers. rmse <- function(params) {   sqrt(sum((df(f$x, params[1], params[2]) - f$y)^2)) }  # L-BFGS-B optimization. o <- optim(c(50, 50),              # Initial parameters.            rmse,            lower=c(0, 0),          # F's degrees of freedom's domain            upper=c(2^16, 2^16),    # is [0,Inf).            method='L-BFGS-B',            control=list(trace=3))  print(o)

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