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SUMMARY:Yuan Zhou (remote) (University of Kentucky)
DTSTART:20251202T233000Z
DTEND:20251203T003000Z
DTSTAMP:20260422T001718Z
UID:SFUOR/58
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/SFUOR/58/">A
 ll Cyclic Group Facets Inject</a>\nby Yuan Zhou (remote) (University of Ke
 ntucky) as part of PIMS-CORDS SFU Operations Research Seminar\n\nLecture h
 eld in ASB 10908.\n\nAbstract\nIn this talk\, we study cut-generating func
 tions in the setting of the Gomory-Johnson group relaxations\nfor integer 
 programming. We address an open question: whether every facet (extreme fun
 ction) for a\nfinite cyclic group relaxation injects into the space of ext
 reme functions for the infinite group problem.  We give a variant of the B
 asu-Hildebrand-Molinaro approximation theorem [IPCO 2016] for\ncontinuous 
 minimal functions of the infinite group problem. Specifically\, we show th
 at any piecewise\nlinear minimal function with rational breakpoints in 1/q
 Z and rational values at these breakpoints can be approximated by piecewis
 e linear two-slope extreme functions while preserving all function values 
 on\n1/qZ: a feature not guaranteed by the earlier construction. As a corol
 lary\, every extreme function for the finite group problem on 1/qZ is the 
 restriction of a continuous piecewise linear two-slope extreme\nfunction f
 or the infinite group problem\, with breakpoints on a refinement 1/(Mq)Z. 
 Combined with\nGomory’s master theorem\, this establishes that the infin
 ite group problem indeed serves as the correct\nmaster problem for facets 
 of one-row group relaxations.\n\nThis is a joint work with Matthias Koeppe
 .\n
LOCATION:https://researchseminars.org/talk/SFUOR/58/
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