Argument `iter` in `optimizing` does not work properly

Summary:

The argument iter in optimizing does not seem to work as expected.

Description:

Summary says it all, see below for reproducible steps.

Reproducible Steps:

Consider simple stan model:

data {
  int n;
  vector[n] x;
}

parameters {
  real mu;
}

model {
  target += normal_lpdf(x | mu, 1);
}

Now if we call optimizing with iter=0 I would expect that the program returns the initial value, but it doesn't.

library(rstan)

# create some synthetic data
set.seed(123)
x <- rnorm(10)+5
model <- stan_model('simple.stan')
data <- list(x=x, n=length(x))

fit <- optimizing(model, data=data, hessian=T, as_vector=F, init=list(mu=0), iter=0)
print(fit$par$mu) # should print 0
print(mean(x)) # just for comparison

This prints

[1] 5.074626
[1] 5.074626

In other words, optimizing optimizes mu to the MAP estimate, so iter has no influence.

A weird thing is that when I change the init, it does not necessarily iterate until MAP is reached.

fit <- optimizing(model, data=data, hessian=T, as_vector=F, init=list(mu=10), iter=0)
print(fit$par$mu) # should print 10
print(mean(x)) # just for comparison

This prints

[1] 9.507463
[1] 5.074626

I stumbled upon this when I tried to evaluate the Hessian of the log posterior with some fixed values of parameters, and thought I could achieve this by fixing iter=0.

RStan Version:

2.19.2

R Version:

"R version 3.6.0 (2019-04-26)"

Operating System:

OS X 10.14.6

Start with the optimizing entry point and run the reproducible R example using simple.stan, init=list(mu=0), and iter=0. Compare the returned parameter with the supplied initial value and verify that zero iterations no longer optimize the parameter while preserving the intended Hessian evaluation behavior.