2 citations · 3 across the 10 of their papers we have counts for
5 papers · 1 filter
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…
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…
Escaping saddle points without Lipschitz smoothness: the power of nonlinear preconditioning
Alexander Bodard, Panagiotis Patrinos
We study generalized smoothness in nonconvex optimization, focusing on -smoothness and anisotropic smoothness. The former was empirically derived from practical neural…
Second-order methods for provably escaping strict saddle points in composite nonconvex and nonsmooth optimization
Alexander Bodard, Masoud Ahookhosh, Panagiotis Patrinos
This study introduces two second-order methods designed to provably avoid saddle points in composite nonconvex optimization problems: (i) a nonsmooth trust-region method and (ii) a…
A localized consensus-based sampling algorithm
Arne Bouillon, Alexander Bodard, Panagiotis Patrinos +2
We propose a localized consensus-based method for sampling from non-Gaussian distributions, a task that frequently arises when solving Bayesian inverse problems. Our method arises…