9 papers · 1 filter
Newton methods beyond Hessian Lipschitz continuity: A nonlinear preconditioning approach
Alexander Bodard, Panagiotis Patrinos
Newton-type methods are typically analyzed under Lipschitz continuity of the Hessian, an assumption that can fail for objectives with higher-order or polynomial growth. We introduc…
Nonlinearly preconditioned gradient flows
Konstantinos Oikonomidis, Alexander Bodard, Jan Quan +1
We study a continuous-time dynamical system which arises as the limit of a broad class of nonlinearly preconditioned gradient methods. Under mild assumptions, we establish existenc…
PANOC-lite: A simpler and more efficient algorithm for composite minimization
Alexander Bodard, Pieter Pas, Andreas Themelis +1
This work introduces a simple and efficient linesearch method for composite minimization that accelerates proximal-gradient iterations with fast Newton-type directions. Our algorit…
EM++: A parameter learning framework for stochastic switching systems
Renzi Wang, Alexander Bodard, Mathijs Schuurmans +1
This paper proposes a general switching dynamical system model, and a custom majorization-minimization-based algorithm EM++ for identifying its parameters. For certain families of…
Scaled relative graphs for pairs of operators beyond classical monotonicity
Jan Quan, Alexander Bodard, Konstantinos Oikonomidis +1
We introduce a generalization of the scaled relative graph (SRG) to pairs of operators, enabling the visualization of their relative incremental properties. This novel SRG framewor…
The inexact power augmented Lagrangian method for constrained nonconvex optimization
Alexander Bodard, Konstantinos Oikonomidis, Emanuel Laude +1
This work introduces an unconventional inexact augmented Lagrangian method where the augmenting term is a Euclidean norm raised to a power between one and two. The proposed algorit…