4 papers · 1 filter
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…
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…