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URL:/combinatorics-and-optimization/events/tutte-colloq
 uium-david-torregrossa-belen
SUMMARY:Tutte colloquium-David Torregrossa Belén
CLASS:PUBLIC
DESCRIPTION:Summary \n\nTITLE:Splitting algorithms for monotone inclusions 
 with\nminimal dimension\n\nSPEAKER:\n David Torregrossa Belén\n\nAFFILIA
 TION:\n Center for Mathematical Modeling\, University of Chile\n\nLOCATIO
 N:\n MC 5501\n\nABSTRACT: Many situations in convex optimization can be mo
 deled as the\nproblem of finding a zero of a monotone operator\, which ca
 n be\nregarded as a generalization of the gradient of a differentiable\nc
 onvex function. In order to numerically address this monotone\ninclusion 
 problem\, it is vital to be able to exploit the inherent\nstructure of th
 e operator defining it. The algorithms in the family\nof the splitting me
 thods achieve this by iteratively solving simpler\nsubtasks that are defi
 ned by separately using some parts of the\noriginal problem.\n\nIn the fi
 rst part of this talk\, we will introduce some of the\nmost relevant mono
 tone inclusion problems and present their\napplications to optimization. 
 Subsequently\, we will draw our\nattention to a common anomaly that has p
 ersisted in the design of\nmethods in this family: the dimension of the u
 nderlying space\n—which we denote as lifting— of the algorithms abnor
 mally\nincreases as the problem size grows. This has direct implications 
 on\nthe computational performance of the method as a result of the\nincre
 ase of memory requirements. In this framework\, we characterize\nthe mini
 mal lifting that can be obtained by splitting algorithms\nadept at solvin
 g certain general monotone inclusions. Moreover\, we\npresent splitting m
 ethods matching these lifting bounds\, and\nthus having minimal lifting.\
 n\n \n 
DTSTAMP:20250711T084638Z
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