Any recommendations for choice of a constrained optimization library suitable for my optimization function? I am minimizing a i) non-linear function with linear equality and inequality constraints, and ii) have available the gradient and the hessian of the function.
If it helps, the function I am minimizing is the Kullback-Liebler divergence.
There are quite a few solutions on the R Cran Task page for Optimization. Iam able to perform the optimization in MATLAB using the fmincon() function which seems to use an interior-point or a trust-region-reflective. Ideally there is a library that is well-suited to the problem defined.
Both packages, alabama and Rsolnp, contain “[i]mplementations of the augmented lagrange multiplier method for general nonlinear optimization” — as the optimization task view says — and are quite reliable and robust. The can handle equality and inequality constraints defined as (nonlinear) functions again.
I have worked with both packages. Sometimes, constraints are a bit easier to formulate with Rsolnp, whereas alabama appears to be a bit faster at times.
There is also the package Rdonlp2 that relies on an external and in the optimization community well-known software library. Unfortunately, its license status is a bit uncertain at the moment.