Continuous Optimization Seminar - Stefan Sremac

Wednesday, November 15, 2017 4:00 pm - 4:00 pm EST (GMT -05:00)

Title: Proximal alternating linearized minimization for nonconvex and nonsmooth problems

Speaker: Stefan Sremac
Affiliation: University of Waterloo
Room: MC 5479


We will be discussing the paper (having the same title) by Jerome Bolte, Shoham Sabach and Marc Teboulle.  We introduce a proximal alternating linearized minimization (PALM) algorithm for solving a broad class of nonconvex and nonsmooth minimization problems. Building on the powerful Kurdyka–Łojasiewicz property, we derive a self-contained convergence analysis framework and establish that each bounded sequence generated by PALM globally converges to a critical point. Our approach allows to analyze various classes of nonconvex-nonsmooth problems and related nonconvex proximal forward–backward algorithms with semi-algebraic problem’s data, the later property being shared by many functions arising in a wide variety of fundamental applications. A by-product of our framework also shows that our results are new even in the convex setting. As an illustration of the results, we derive a new and simple globally convergent algorithm for solving the sparse nonnegative matrix factorization problem.