Question

I have a complex objective function I am looking to optimize. The optimization problem takes a considerable time to optimize. Fortunately, I do have the gradient and the hessian of the function available.

Is there an optimization package in R that can take all three of these inputs? The class ‘optim’ does not accept the Hessian. I have scanned the CRAN task page for optimization and nothing pops.

For what it’s worth, I am able to perform the optimization in MATLAB using ‘fminunc‘ with the the ‘GradObj’ and ‘Hessian’ arguments.

Answer 1

I think the package trust which does trust region optimization will do the trick. From the documentation of trust, you see that

This function carries out a minimization or maximization of a function
using a trust region algorithm… (it accepts) an R function that
computes value, gradient, and Hessian of the function to be minimized
or maximized and returns them as a list with components value,
gradient, and hessian.

In fact, I think it uses the same algorithm used by fminunc.

By default fminunc chooses the large-scale algorithm if you supply the
gradient in fun and set GradObj to ‘on’ using optimset. This algorithm
is a subspace trust-region method and is based on the
interior-reflective Newton method described in [2] and [3]. Each
iteration involves the approximate solution of a large linear system
using the method of preconditioned conjugate gradients (PCG). See
Large Scale fminunc Algorithm, Trust-Region Methods for Nonlinear
Minimization and Preconditioned Conjugate Gradient Method.