3 papers
math.OC2025
Convergence rates of Newton's method for strongly self-concordant minimization
Nick Tsipinakis, Panos Parpas
Newton's method has been thoroughly studied for the class of self-concordant functions. However, a local analysis specific to strongly self-concordant functions (a subclass of the…
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…