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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…
math.OC2023
Adaptive Multilevel Newton: A Quadratically Convergent Optimization Method
Nick Tsipinakis, Panagiotis Tigkas, Panos Parpas
Newton's method may exhibit slower convergence than vanilla Gradient Descent in its initial phase on strongly convex problems. Classical Newton-type multilevel methods mitigate thi…