mize_step: One Step of Optimization

In jlmelville/mizer: Unconstrained Numerical Optimization Algorithms

One Step of Optimization

Description

Performs one iteration of optimization using a specified optimizer.

Usage

mize_step(opt, par, fg)

Arguments

opt	Optimizer, created by make_mize.
par	Vector of initial values for the function to be optimized over.
fg	Function and gradient list. See the documentation of mize.

Details

This function returns both the (hopefully) optimized vector of parameters, and an updated version of the optimizer itself. This is intended to be used when you want more control over the optimization process compared to the more black box approach of the mize function. In return for having to manually call this function every time you want the next iteration of optimization, you gain the ability to do your own checks for convergence, logging and so on, as well as take other action between iterations, e.g. visualization.

Normally calling this function should return a more optimized vector of parameters than the input, or at least leave the parameters unchanged if no improvement was found, although this is determined by how the optimizer was configured by make_mize. It is very possible to create an optimizer that can cause a solution to diverge. It is the responsibility of the caller to check that the result of the optimization step has actually reduced the value returned from function being optimized.

Details of the fg list can be found in the 'Details' section of mize.

Value

Result of the current optimization step, a list with components:

• opt. Updated version of the optimizer passed to the opt argument Should be passed as the opt argument in the next iteration.

• par. Updated version of the parameters passed to the par argument. Should be passed as the par argument in the next iteration.

• nf. Running total number of function evaluations carried out since iteration 1.

• ng. Running total number of gradient evaluations carried out since iteration 1.

• f. Optional. The new value of the function, evaluated at the returned value of par. Only present if calculated as part of the optimization step (e.g. during a line search calculation).

• g. Optional. The gradient vector, evaluated at the returned value of par. Only present if the gradient was calculated as part of the optimization step (e.g. during a line search calculation.)

See Also

make_mize to create a value to pass to opt, mize_init to initialize opt before passing it to this function for the first time. mize creates an optimizer and carries out a full optimization with it.

Examples

rosenbrock_fg <- list(
  fn = function(x) {
    100 * (x[2] - x[1] * x[1])^2 + (1 - x[1])^2
  },
  gr = function(x) {
    c(
      -400 * x[1] * (x[2] - x[1] * x[1]) - 2 * (1 - x[1]),
      200 * (x[2] - x[1] * x[1])
    )
  }
)
rb0 <- c(-1.2, 1)

opt <- make_mize(
  method = "SD", line_search = "const", step0 = 0.0001,
  par = rb0, fg = rosenbrock_fg
)
par <- rb0
for (iter in 1:3) {
  res <- mize_step(opt, par, rosenbrock_fg)
  par <- res$par
  opt <- res$opt
}

jlmelville/mizer documentation built on Jan. 27, 2025, 8:33 a.m.