Toolkit for Advanced Optimization (TAO) Bindings for R

taoR is an R package which lets you use the TAO library from R. TAO is a library of optimization algorithms. Among them is Pounders. Pounders can be a useful tool for economists who estimate structural models using indirect inference, because unlike commonly used algorithms such as Nelder-Mead, Pounders is tailored for minimizing a non-linear sum of squares objective function, and therefore may require fewer iterations to arrive at a local optimum than Nelder-Mead. For more details, see here and here.

Please note that this package is currently a work in progress.

Install

TAO is part of PETSc. If you do not have PETSc installed on your system, then taoR will attempt to install PETSc for you. There are two different ways to install taoR.

1. Build PETSc binaries as part of package installation

PETSc will be compiled using the same set of compilers that R uses. Building the PETSc binaries will take several minutes.

source("http://jtilly.io/taoR/install_taoR.R")
install_taoR(compile_binaries = TRUE)

2. Use existing PETSc installation

See here for detailed instructions on how to install PETSc.

source("http://jtilly.io/taoR/install_taoR.R")
install_taoR(PETSC_DIR = "/path/to/petsc", PETSC_ARCH = "...")

Note that taoR copies the PETSc binary into the R package directory. Installing the package this way may require manual adjustment of the flags in src/Makevars.in before installation.

Example

We minimize the objective function (x[1] - 3) ^ 2 + (x[2] + 1) ^ 2 with respect to x. The syntax is similar to R's optim function.

library("taoR")

# the objective function is (x[1] - 3) ^ 2 + (x[2] + 1) ^2 
# with solution vector c(3, -1)

# use pounders
objfun = function(x) c((x[1] - 3), (x[2] + 1))
ret = tao(par = c(1, 2),
                fn = objfun, 
                method = "pounders", 
                control = list("tao_pounders_gqt" = ""))
ret$x
# [1]  3 -1
ret$iterations
# [1] 7

    
# use Nelder-Mead
objfun = function(x) sum(c((x[1] - 3), (x[2] + 1))^2)
ret = tao(par = c(1, 2),
                fn = objfun, 
                method = "nm", 
                control = list())
ret$x
# [1]  3.005468 -1.004479
ret$iterations
# [1] 20

Available Optimization Algorithms

The parameter method can be set to one of the following optimizers.

• nls: Newton's method with line search for unconstrained minimization
• ntr: Newton's method with trust region for unconstrained minimization
• ntl: Newton's method with trust region, line search for unconstrained minimization
• lmvm: Limited memory variable metric method for unconstrained minimization
• cg: Nonlinear conjugate gradient method for unconstrained minimization
• nm: Nelder-Mead algorithm for derivate-free unconstrained minimization
• tron: Newton Trust Region method for bound constrained minimization
• gpcg: Newton Trust Region method for quadratic bound constrained minimization
• blmvm: Limited memory variable metric method for bound constrained minimization
• pounders: Derivative-free model-based algorithm for nonlinear least squares