The principle of data minimization aims to reduce the amount of data
collected, processed or retained to minimize the potential for misuse,
unauthorized access, or data breaches. Rooted in privacy-by-design principles,
data minimization has been endorsed by various global data protection
regulations. However, its practical implementation remains a challenge due to
the lack of a rigorous formulation. This paper addresses this gap and
introduces an optimization framework for data minimization based on its legal
definitions. It then adapts several optimization algorithms to perform data
minimization and conducts a comprehensive evaluation in terms of their
compliance with minimization objectives as well as their impact on user
privacy. Our analysis underscores the mismatch between the privacy expectations
of data minimization and the actual privacy benefits, emphasizing the need for
approaches that account for multiple facets of real-world privacy risks