While optimization is well studied for real-valued functions $f : \mathbb{R}^{N} \to \mathbb{R}$, many physical problems are (partially) specified in terms of complex-valued functions $f_{c} : \mathbb{C}^{N} \to \mathbb{C}^{M}$. Current optimization packages have limited support for such functions. In particular it is unclear how to define algorithmic differentiation w.r.t. complex-valued functions and arguments. This document is a collection of working notes on the topic.