This function implements the simulated annealing algorithm, which is a global optimization algorithm that is useful for finding a good starting point for a local optimization algorithm. We do not return this as an MLE object because, to be a good estimate of the MLE, the gradient of `f` evaluated at its solution should be close to zero, assuming the MLE is interior to the domain of `f`. However, since this algorithm is not guided by gradient information, it is not sensitive to the gradient of `f` and instead only seeks to maximize `f`.

This function implements the simulated annealing algorithm, which is a global optimization algorithm that is useful for finding a good starting point for a local optimization algorithm. We do not return this as an MLE object because, to be a good estimate of the MLE, the gradient of `f` evaluated at its solution should be close to zero, assuming the MLE is interior to the domain of `f`. However, since this algorithm is not guided by gradient information, it is not sensitive to the gradient of `f` and instead only seeks to maximize `f`.

Usage

sim_anneal(par, fn, control = list(), ...)

Arguments

par

Initial guess

fn

Objective function to maximize

control

List of optional arguments

...

Additional arguments that may be passed; loads into options, and is also passed into `neigh`

Value

list, members include: `par`: best solution `value`: function value `fn(par)` `fn_count`: a count of `fn` invocations `accepted`: a count of accepted moves `trace_info`: a matrix of trace information (optional)

Functions

• sim_anneal(): control

Fields

t_init

Initial temperature, defaults to 100

t_end

Final temperature, defaults to 0

alpha

Numberic, cooling factor, defaults to .95

REPORT

The frequency of reports if control$debug > 0. Defaults to every 100 iterations.

it_per_temp

Ineger, iterations per temperature, defaults to 100

maxit

Integer, maximum number of iterations, defaults to 100000

accept_p

Acceptance probability function, defaults to `runif(1) < exp((val0 - val1) / temp)`, where `val0` is the function value at the current position and `val1` is the function value at the proposed position. We pass `temp` (temperature), `val1` (new value at candidate position `par1`), `val0` (old value at current position), `it` (iteration), and `...` as arguments to `accept_p`.

fnscale

Scaling factor for `fn`, defaults to 1. If negative, then turns the problem into a maximization problem.

sup

Support function, returns TRUE if `par` is in the domain of `fn`

proj

Projection function, returns a vector in the domain of `fn`

neigh

Neighborhood function, returns a random neighbor of `par`, defaults to `par + rnorm(length(par))`. We pass `par` `temp`, `it`, `value`, and `...` as arguments to `neigh`.

trace

logical, whether to store current changes in position and associated other values in a `trace_info` matrix.