6 papers · 1 filter
Adaptive Multilevel Newton: A Quadratically Convergent Optimization Method
Nick Tsipinakis, Panos Parpas, Matthias Voigt
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…
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…
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…
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…
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…
A Multilevel Method for Self-Concordant Minimization
Nick Tsipinakis, Panos Parpas
The analysis of second-order optimization methods based either on sub-sampling, randomization or sketching has two serious shortcomings compared to the conventional Newton method.…