trustOptim is an R package for unconstrained optimization of nonlinear objective functions with sparse Hessians. You should consider using this package if:

  • you are optimizing over a large number of parameters;
  • you are able to provide a function that computes the gradient of the function analytically;
  • the Hessian of the objective function is sparse (i.e., there are relatively few nonzero cross-partial derivatives), and you can provide a function that computes the Hessian.
  • you desire the stability of a trust region optimization algorithm; and
  • you want an optimization algorithm that uses the norm of the gradient being zero (and not heuristics like “is the objective function making progress) as a stopping rule.

A common use case for a sparse Hessian is a hierarchical model that assumes conditional independences across heterogeneous units. Even if the Hessian is not sparse, and/or it is hard to compute the Hessian analytically, this package does support BFGS and SR1 updates instead. But the real benefit of this package comes from exploiting the sparsity of the Hessian of the objective function.

Getting the package

The latest release version is available on CRAN. You should be able to install it with a simple


The source code is available at .

Using the package

The trust.optim function calls the optimizer.

The objective function is defined by three R functions, all of which take a numeric vector as the first argument.

  • f: provides the objective function as a numeric scalar value
  • grad: provides the gradient as a numeric vector
  • hess: provides the Hessian as a dsCMatrix object (from the Matrix package).

Starting from parameter vector x, to minimize a function f, call

opt <- trust.optim(x, f, grad, hess, method="Sparse")

See the vignettes for examples, and the package manual for details, options, etc.