BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Jiajin Li (UBC Sauder) DTSTART:20250123T220000Z DTEND:20250123T230000Z DTSTAMP:20260513T201628Z UID:SFUOR/46 DESCRIPTION:Title: U nveiling Spurious Stationarity and Hardness Results for Bregman Proximal-T ype Algorithms\nby Jiajin Li (UBC Sauder) as part of PIMS-CORDS SFU Op erations Research Seminar\n\nLecture held in ASB 10908.\n\nAbstract\nBregm an proximal-type algorithms\, such as mirror descent\, are popular in opti mization and data science for effectively exploiting problem structures an d optimizing them under tailored geometries. However\, most of existing co nvergence results rely on the gradient Lipschitz continuity of the kernel\ , which unfortunately excludes most commonly used cases\, such as the Shan non entropy. In this paper\, we reveal a fundamental limitation of these m ethods:  Spurious stationary points inevitably arise when the kernel is n ot gradient Lipschitz. The existence of these spurious stationary points l eads to an algorithm-dependent hardness result: Bregman proximal-type algo rithms cannot escape from a spurious stationary point within any finite nu mber of iterations when initialized from that point\, even in convex setti ngs. This limitation is discovered through the lack of a well-defined stat ionarity measure based on Bregman divergence for non-gradient Lipschitz ke rnels. Although some extensions attempt to address this issue\, we demonst rate that they still fail to reliably distinguish between stationary and n on-stationary points for such kernels. Our findings underscore the need fo r new theoretical tools and algorithms in Bregman geometry\, paving the wa y for further research.\n LOCATION:https://researchseminars.org/talk/SFUOR/46/ END:VEVENT END:VCALENDAR