A dual approach to PhaseLift via gauge programming and bundle methods

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 matrix-lifting approach taken by PhaseLift for phase retrieval results in a problem where the number of variables is quadratic in the number of constraints. We consider a duality framework and numerical methods to leverage the relatively small number of constraints. Preliminary numerical results illustrate our approach and its flexibility.