Gainesville: Dr. Guanghui Lan, Assistant Professor of Industrial & Systems Engineering will deliver the graduate seminar on the topic entitled, “Level Methods Uniformly Optimal for Composite and Structured NonSmooth Convex Optimization” being held on Thurs, Nov 3, 2011 at 4:05 p.m. in McCarthy Hall A, Room 2186.
The main goal of this talk is to present uniformly optimal first-order methods for large-scale convex programming (CP). By uniform optimality we mean that the first-order methods themselves do not require the input of any problem parameters, but can still achieve the best possible iteration complexity bounds. To this end, we develop new level-type methods and demonstrate that they can uniformly achieve the optimal iteration complexity for solving a class of generalized composite CP problems, which covers nonsmooth, weakly smooth, smooth, minmax, composite and regularized CP problems etc. We then present two variants of this level method for solving a class of bilinear saddle point problems and show that one of these variants can achieve the optimal iteration complexity without requiring the input of any problem parameters. We illustrate the significant advantages of these level methods over some existing first-order methods for solving certain important classes of semidefinite programming (SDP) and two-stage stochastic programming (SP) problems.