mize

Unconstrained Numerical Optimization Algorithms.

mize can be used as a standalone function like the stats::optim function, or can be integrated into other packages by creating a stateful optimizer and handling the iterations, convergence, logging and so on externally.

mize knows how to do Broyden-Fletcher-Goldfarb-Shanno (BFGS), the limited-memory BFGS (L-BFGS), various flavors of Conjugate Gradient (CG), Nesterov Accelerated Gradient (NAG) and momentum-based methods, among others.

Installing

# Install from CRAN:
install.packages("mize")

# Or install the development version from GitHub:
# install.packages("devtools")
devtools::install_github("jlmelville/mize")

Documentation

?mize

There are also some vignettes:

• mize.Rmd, which goes through many of the options available.
• mmds.Rmd, which does a simple, but non-trivial, application of mize to carry out metric Multi-Dimensional Scaling on the eurodist data set.
• stateful.Rmd, which demonstrates how to use mize statefully, so you can manually and externally invoke each iteration step.

Examples

# Make a list containing the function and gradient:
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])) })
# Starting point:
rb0 <- c(-1.2, 1)

# Minimize using L-BFGS
res <- mize(rb0, rosenbrock_fg, method = "L-BFGS")
# Optimized parameters are in res$par

# Or create an optimizer and then loop manually
opt <- make_mize(method = "L-BFGS")
opt <- mize_init(opt, rb0, rosenbrock_fg)

par <- rb0
done <- FALSE
iter <- 0
while (!done) {
  iter <- iter + 1
  res <- mize_step(opt, par, rosenbrock_fg)
  par <- res$par
  opt <- res$opt
  # Look at res$f for current function value
  # you get to (i.e. have to) decide when to stop
  done <- iter > 30
}

See also

The Wolfe line searches use conversion of Mark Schmidt's minFunc routines, Carl Edward Rasmussen's Matlab code and Dianne O'Leary's Matlab translation of the Moré-Thuente line search algorithm from MINPACK.

I also maintain the funconstrain package, which contains a large number of test problems for numerical optimization. See this gist for functions to use mize with funconstrain.

License

BSD 2-Clause.

Acknowledgments

I am grateful to Hans Werner Borchers, who provided assistance and encouragement in getting mize onto CRAN.