BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Mingyi Hong 洪明毅 (University of Minnesota) DTSTART:20201229T070000Z DTEND:20201229T081500Z DTSTAMP:20260423T024030Z UID:iccm2020/74 DESCRIPTION:Title: Convergence Analysis of Alternating Direction Method of Multipliers for a Family of Nonconvex Problems\nby Mingyi Hong 洪明毅 (University o f Minnesota) as part of ICCM 2020\n\n\nAbstract\nThe alternating direction method of multipliers (ADMM) is widely used to solve large-scale linearly constrained optimization problems\, convex or nonconvex\, in many enginee ring fields. However there is a general lack of theoretical understanding of the algorithm when the objective function is nonconvex. In this work we analyze the convergence of the ADMM for solving certain nonconvex consens us and sharing problems. By using a three-step argument\, we show that the classical ADMM converges to the set of stationary solutions\, provided th at the penalty parameter in the augmented Lagrangian is chosen to be suffi ciently large. For the sharing problems\, we show that the ADMM is converg ent regardless of the number of variable blocks. Our analysis does not imp ose any assumptions on the iterates generated by the algorithm\, and is br oadly applicable to many ADMM variants involving proximal update rules and various flexible block selection rules. Finally\, we discuss a few genera lizations of the three-step analysis to a broader class of algorithms\, wi th applications in signal processing and machine learning.\n LOCATION:https://researchseminars.org/talk/iccm2020/74/ END:VEVENT END:VCALENDAR