2 citations · 3 across the 10 of their papers we have counts for
12 papers
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…
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…
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…
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…
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…
Global Convergence Analysis of the Power Proximal Point and Augmented Lagrangian Method
Konstantinos A. Oikonomidis, Alexander Bodard, Emanuel Laude +1
In this paper we study an unconventional inexact Augmented Lagrangian Method (ALM) for convex optimization problems, as first proposed by Bertsekas, wherein the penalty term is a p…
PANTR: A proximal algorithm with trust-region updates for nonconvex constrained optimization
Alexander Bodard, Pieter Pas, Panagiotis Patrinos
This work presents PANTR, an efficient solver for nonconvex constrained optimization problems, that is well-suited as an inner solver for an augmented Lagrangian method. The propos…
SPOCK: A proximal method for multistage risk-averse optimal control problems
Alexander Bodard, Ruairi Moran, Mathijs Schuurmans +2
Risk-averse optimal control problems have gained a lot of attention in the last decade, mostly due to their attractive mathematical properties and practical importance. They can be…