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URL:https://uwaterloo.ca/combinatorics-and-optimization/events/tutte-colloq
 uium-david-torregrossa-belen
SUMMARY:Tutte colloquium-David Torregrossa Belén
CLASS:PUBLIC
DESCRIPTION:TITLE:Splitting algorithms for monotone inclusions with\nminima
 l dimension\n\nSPEAKER:\n David Torregrossa Belén\n\nAFFILIATION:\n Cent
 er for Mathematical Modeling\, University of Chile\n\nLOCATION:\n MC 5501
 \n\nABSTRACT: Many situations in convex optimization can be modeled as the
 \nproblem of finding a zero of a monotone operator\, which can be\nregard
 ed as a generalization of the gradient of a differentiable\nconvex functi
 on. In order to numerically address this monotone\ninclusion problem\, it
  is vital to be able to exploit the inherent\nstructure of the operator 
 defining it. The algorithms in the family\nof the splitting methods achie
 ve this by iteratively solving simpler\nsubtasks that are defined by sepa
 rately using some parts of the\noriginal problem.\n\nIn the first part of 
 this talk\, we will introduce some of the\nmost relevant monotone inclusi
 on problems and present their\napplications to optimization. Subsequently
 \, we will draw our\nattention to a common anomaly that has persisted in 
 the design of\nmethods in this family: the dimension of the underlying sp
 ace\n—which we denote as lifting— of the algorithms abnormally\nincre
 ases as the problem size grows. This has direct implications on\nthe comp
 utational performance of the method as a result of the\nincrease of memor
 y requirements. In this framework\, we characterize\nthe minimal lifting 
 that can be obtained by splitting algorithms\nadept at solving certain ge
 neral monotone inclusions. Moreover\, we\npresent splitting methods match
 ing these lifting bounds\, and\nthus having minimal lifting.\n\n 
DTSTAMP:20260402T161853Z
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