Garud Iyengar: Feb 13

Title: Fast first-order augmented Lagrangian algorithms for sparse optimization problems

Abstract:

In this talk we will survey recent work on fast first-order algorithms for solving optimization problems with non-trivial conic constraints. These algorithms are augmented Lagrangian algorithms; however, unlike traditional augmented Lagrangian algorithms we update the penalty multiplier during the course of the algorithm. The algorithm iterates are epsilon-feasible and epsilon-optimal in O(log(1/epsilon))-multiplier update steps with an overal complexity of O(1/epsilon). We will discuss the key steps in the algorithm development and show numerical results for basis pursuit, principal component pursuit and stable principal component pursuit.

Joint work with N. Serhat Aybat (Penn State)