In mrparker909/optimizeAPA: An R Package for Arbitrary Precision Optimization of Multi-parameter Functions

optimizeAPA

Arbitrary Precision Arithmetic (APA) optimization algorithms implemented in R.

Throughout I will use the abreviations APA = "arbitrary precision arithmetic", and NAPA="non arbitrary precision arithmetic".

The APA in this package is achieved using the packages Rmpfr and gmp.

Installation

install.packages("devtools")
devtools::install_github("mrparker909/optimizeAPA")

Currently Implemented:

• optim_DFP_NAPA (non-APA version of DFP algorithm)
• optim_DFP_APA (APA version of DFP algorithm)

Currently In Progress:

• optim_BFGS_NAPA (non-APA version of BFGS algorithm)
• optim_BFGS_APA (APA version of BFGS algorithm)

Some Illustrative Examples

optimDFP_APA

library(optimizeAPA)

# notice that the function must be made using APA arithmetic from the package Rmpfr
# the function inputs are first: the parameter to be optimized over (x)
# and must also include the variable precBits, to be passed to all APA numbers.
# Any other function parameters (such as center) can be passed to the function
# when calling optim_DFP_APA

# function we would like to optimize:
quadratic <- function(x, center, precBits=64) {
  x_apa <- Rmpfr::mpfr(x,precBits) # convert input to APA
  (x_apa-center)^2
}

# APA optimization
optim_DFP_APA(starts=0, func=quadratic, center=10, precBits = 64)

The minimum is attained at $x_{min}=10$, where the function is found to be $f(x_{min})=0$, and the gradient is $grad(f(x_{min})) = 0$.

We can compare these results to the optim_DFP_NAPA results, and to the regular optim results:

# function we would like to optimize:
quadratic_NAPA <- function(x, center) {
  (x-center)^2
}

# NAPA optimization
optim_DFP_NAPA(starts=0, func=quadratic_NAPA, center=10)
optim(par=0, fn=quadratic_NAPA, hessian=TRUE, method="BFGS", center=10)

It can be desirable to retain the convergence path for diagnosis and visualization purposes. This can be done easily with both the APA and NAPA version of the optimization algorithm:

library(ggplot2) # ggplot for plotting

# just set keepValues to TRUE to keep every visited value
op <- optim_DFP_NAPA(starts=0, func=quadratic_NAPA, center=10, keepValues = TRUE)

# convergence path plot:
plotConvergence(op) + ggtitle("Convergence Path")

And the same for the APA version:

# just set keepValues to TRUE to keep every visited value
op <- optim_DFP_APA(starts=0, func=quadratic, center=10, keepValues = TRUE)

# convergence path plot:
plotConvergence(op)

How to Cite

Parker, M.R.P. (2020). optimizeAPA: An R Package for Arbitrary Precision Optimization of Multi-parameter Functions. R package version r packageVersion("optimizeAPA"). https://github.com/mrparker909/optimizeAPA

mrparker909/optimizeAPA documentation built on June 28, 2020, 3:57 p.m.