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DTSTAMP:20260407T124520
DTSTART;TZID=America/Detroit:20261007T160000
DTEND;TZID=America/Detroit:20261007T170000
SUMMARY:Workshop / Seminar:Robust and Risk-Sensitive Acceleration in Gradient Methods
DESCRIPTION:First-order methods such as gradient descent (GD) are foundational in optimization. In unconstrained problems with exact gradients\, momentum-based methods—most notably Nesterov’s accelerated gradient descent (AGD) and Polyak’s heavy-ball (HB) method—achieve faster convergence by improving dependence on the condition number. However\, this acceleration comes at a cost: momentum amplifies gradient noise\, making these methods less robust than GD under standard parameter choices and requiring more accurate gradient estimates to attain comparable accuracy. Similar challenges arise in convex and nonconvex min–max optimization.\nMotivated by applications in machine learning\, this talk studies unconstrained and min–max optimization under deterministic\, unbiased stochastic\, and biased stochastic gradient noise. I will present new algorithms that achieve optimal robustness against different noise types\, using control-theoretic tools such as the H_2​ norm\, the H_∞​ norm\, and the risk-sensitivity index\, together with coherent risk measures. I will also discuss worst-case noise constructions and high-probability convergence guarantees. This perspective builds a bridge between optimization and robust control theory and enables the design of noise-robust and risk-sensitive accelerated methods.\nRepresentative Publications:\nM. Gürbüzbalaban\, Y. Syed\, N. S. Aybat\, Accelerated gradient methods with biased gradient estimates: Risk sensitivity\, high-probability guarantees\, and large deviation bounds\, Journal of Nonlinear and Variational Analysis\, 2026 (Special Issue). https://jnva.biemdas.com/archives/2927\nM. Gürbüzbalaban\, Robustly Stable Accelerated Momentum Methods with a Near-Optimal L_2​ Gain and H_∞​ Performance\, Mathematics of Operations Research\, 2025.\nhttps://pubsonline.informs.org/doi/abs/10.1287/moor.2023.0321\nB. Can and M. Gürbüzbalaban\, Entropic risk-averse generalized momentum methods\, Optimization Methods and Software\, 2025. https://www.tandfonline.com/doi/abs/10.1080/10556788.2025.2549356
UID:141373-21888712@events.umich.edu
URL:https://events.umich.edu/event/141373
CLASS:PUBLIC
STATUS:CONFIRMED
CATEGORIES:Mathematics
LOCATION:East Hall - 1360
CONTACT:
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BEGIN:VEVENT
DTSTAMP:20261004T213053
DTSTART;TZID=America/Detroit:20261007T160000
DTEND;TZID=America/Detroit:20261007T170000
SUMMARY:Workshop / Seminar:Student AIM Seminar: Modelling Fusion Plasma Using COGENT
DESCRIPTION:Commercially viable fusion reactors have long been the holy grail of clean energy\nproduction. They promise to capture the same physical process as the sun to provide stable\, safe energy with no direct carbon emissions. Tokamak reactors are one of the leading reactor designs\,\nand require heating a Deuterium-Tritium plasma to nearly 150 million Kelvin\, roughly 10 times hotter than the Sun’s core. This style of reactor contains the superheated plasma via extreme magnetic fields\, as any known material cannot consistently withstand these temperatures. Modelling tokamak plasma presents significant mathematical and computational challenges. The\nplasma evolves nonlinearly through high dimensional phase space\, making high performance computing simulations necessary. The edge region is particularly difficult to simulate due to high\ntemperature gradients and complex geometry. In this seminar\, I will give an overview of COGENT: a mapped\, multiblock\, finite volume code designed to simulate plasma in the edge region of a tokamak. I will talk about the foundational physics and computational mathematics involved\, as well as the current state of the code and possible future extensions.
UID:153245-21915524@events.umich.edu
URL:https://events.umich.edu/event/153245
CLASS:PUBLIC
STATUS:CONFIRMED
CATEGORIES:Applied Mathematics
LOCATION:East Hall - 3088
CONTACT:
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