Argonne National Laboratory

Upcoming Events

Fast Methods for Nonsmooth Nonconvex Problems using Variable Projection

LANS Informal Seminar
Aleksandr Aravkin, University of Washington
May 16, 2018 10:30AM to 11:30AM
Building 240, Room 4301

Abstract: Classic inverse problems are formulated by using smooth penalties and regularizations. However, nonsmooth and nonconvex penalties/regularizers have proved to be extremely useful in underdetermined and noisy settings. Problems with these features also arise naturally when modeling complex physical and chemical phenomena, including PDE-constrained optimization, phase retrieval, and structural resolution of biomolecular models.

We propose a new technique for solving a broad range of nonsmooth, nonconvex problems. The technique is based on a relaxed reformulation and can be implemented on a range of problems in a simple and scalable way. In particular, we typically need only solve least-squares problems, as well as implement custom separable operators. We discuss the problem class, reformulation, and algorithms and give numerous examples of very promising numerical results in different applications.

This seminar will be streamed.