ALOP Colloquium with Sonja Steffensen

On Monday, January 20, 2025 at 16:00 c.t. Dr. Sonja Steffensen, RWTH Aachen, will speak at the ALOP Colloquium about her recent work.

Relaxation Approaches for Nonlinear Sparse Optimization Problems

Abstract:

In many applications, sparse solutions are favoured over non-sparse solutions with comparable objective value, as for example in statistical and deep learning applications. One approach to induce sparsity relies on the l_0 norm as an additional term in the objective. Often this semicontinuous function is approximated using the continuous and convex l_1-norm as a surrogate function instead. However, this can lead to suboptimal results with respect to the sparsity properties of the solution.

In this talk, we will present an alternative exact reformulation (with respect to the l_0 norm)  using non-smooth nonlinear functions to formulate the minimization of the number of non-zero entries. The resulting problem is similar (but not equivalent) to the class of mathematical programs with complementarity constraints (MPCC). As for MPCCs relaxing the problem to a standard nonlinear program we can then apply a general nonlinear solver. In our talk we will discuss and relate the relations between the different reformulations in particular with respect to the original problem. Furthermore, we accompany the theoretical results by some numerical tests using randomly generated data sets.

Please join us at 16:00 c.t. in HS 9.