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math.OC2024
Multilevel Regularized Newton Methods with Fast Convergence Rates
Nick Tsipinakis, Panos Parpas
We introduce new multilevel methods for solving large-scale unconstrained optimization problems. Specifically, the philosophy of multilevel methods is applied to Newton-type method…
math.OC2023
Simba: A Scalable Bilevel Preconditioned Gradient Method for Fast Evasion of Flat Areas and Saddle Points
Nick Tsipinakis, Panos Parpas
The convergence behaviour of first-order methods can be severely slowed down when applied to high-dimensional non-convex functions due to the presence of saddle points. If, additio…