Mathematical optimization has always been at the heart of engineering, statistics, and
economics. In these applied domains, optimization concepts and methods have often been …

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 …

This paper is devoted to the theoretical and numerical investigation of an augmented
Lagrangian method for the solution of optimization problems with geometric constraints …

The sparse portfolio selection problem is one of the most famous and frequently studied
problems in the optimization and financial economics literatures. In a universe of risky …

In a number of application areas, it is desirable to obtain sparse solutions. Minimizing the
number of nonzeroes of the solution (its l0-norm) is a difficult nonconvex optimization …

In optimal control, switching structures demanding at most one control to be active at any
time instance appear frequently. Discretizing such problems, a so-called mathematical …

Recovering sparse signals from linear measurements has demonstrated outstanding utility
in a vast variety of real-world applications. Compressive sensing is the topic that studies the …

The evaluation of time and frequency domain measures of coupling and causality relies on
the parametric representation of linear multivariate processes. The study of temporal …

Recently, a new approach to tackle cardinality-constrained optimization problems based on
a continuous reformulation of the problem was proposed. Following this approach, we …

Nonconvex penalty methods for sparse modeling in linear regression have been a topic of
fervent interest in recent years. Herein, we study a family of nonconvex penalty functions that …