From Feature Selection to Constrained Optimization: A Descent–Ascent Method for Nonsmooth DC Problems – Narges Araboljadidi (University of Campania “Luigi Vanvitelli,” Italy)

Many problems in data analysis and machine learning lead to optimization problems that are neither smooth nor convex. A flexible framework for such problems is difference-of-convex (DC) programming, in which the objective is written as a difference of two convex functions.

This talk begins with a concrete example—feature selection in classification—and shows how it gives rise naturally to a nonsmooth DC problem. We then review the Descent–Ascent algorithm (DADC), which exploits this structure by seeking a direction that decreases one convex part while increasing the other, using only limited first-order information.

The core of the talk treats the harder case in which the constraints, not only the objective, are themselves DC and nonsmooth. We present an extension—the Constrained Descent–Ascent algorithm (CDADC)—to describe the techniques used to incorporate the constraints and establish finite termination of the method. The method is illustrated with numerical examples.