  We present ensmallen, a fast and flexible C++ library for mathematical
optimization of arbitrary user-supplied functions, which can be applied to many
machine learning problems. Several types of optimizations are supported,
including differentiable, separable, constrained, and categorical objective
functions. The library provides many pre-built optimizers (including numerous
variants of SGD and Quasi-Newton optimizers) as well as a flexible framework
for implementing new optimizers and objective functions. Implementation of a
new optimizer requires only one method and a new objective function requires
typically one or two C++ functions. This can aid in the quick implementation
and prototyping of new machine learning algorithms. Due to the use of C++
template metaprogramming, ensmallen is able to support compiler optimizations
that provide fast runtimes. Empirical comparisons show that ensmallen is able
to outperform other optimization frameworks (like Julia and SciPy), sometimes
by large margins. The library is distributed under the BSD license and is ready
for use in production environments.
