8 papers · 1 filter
On the Regularity of Generalized Conjugate Functions
Konstantinos Oikonomidis, Emanuel Laude, Panagiotis Patrinos
We investigate regularity properties of generalized conjugate functions induced by a general coupling function and the associated generalized proximal mapping. Our main results pro…
All roads lead to Rome: Path-following Augmented Lagrangian Methods via Bregman Proximal Regularization
Emanuel Laude
We study Bregman proximal augmented Lagrangian methods with second-order oracles for convex convex-composite optimization problems. The outer loop is an instance of the Bregman pro…
Anisotropic Proximal Point Algorithm
Emanuel Laude, Panagiotis Patrinos
In this paper we study a nonlinear dual space preconditioning approach for the relaxed Proximal Point Algorithm (PPA) with application to monotone and relatively cohypomonotone inc…
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…
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…
Nonlinearly Preconditioned Gradient Methods under Generalized Smoothness
Konstantinos Oikonomidis, Jan Quan, Emanuel Laude +1
We analyze nonlinearly preconditioned gradient methods for solving smooth minimization problems. We introduce a generalized smoothness property, based on the notion of abstract con…