A Dual Approach to Sparse Optimization

A feature common to many sparse optimization problems is that the number of variables may be significantly larger than the number of constraints—e.g., the standard matrix-lifting approach for binary optimization results in a problem where the number of variables is quadratic in the number of constraints. We consider a duality framework applicable to a wide range of nonsmooth sparse optimization problems that allows us to leverage the relatively small number of constraints. Preliminary numerical results illustrate our approach and its flexibility.