Cardinality Minimization, Constraints, and Regularization: A Survey

Understand

We survey optimization problems that involve the cardinality of variable vectors in constraints or the objective function.

• We provide a unified viewpoint on the general problem classes and models, and give concrete examples from diverse application fields such as signal and image processing, portfolio selection, or machine learning.
• The paper discusses general-purpose modeling techniques and broadly applicable as well as problem-specific exact and heuristic solution approaches.
• While our perspective is that of mathematical optimization, a main goal of this work is to reach out to and build bridges between the different communities in which cardinality optimization problems are frequently encountered.