Related papers: Regularizing with Bregman-Moreau envelopes

Tikhonov regularization involves minimizing the combination of a data discrepancy term and a regularizing term, and is the standard approach for solving inverse problems. The use of non-convex regularizers, such as those defined by trained…

Modern imaging methods rely strongly on Bayesian inference techniques to solve challenging imaging problems. Currently, the predominant Bayesian computation approach is convex optimisation, which scales very efficiently to high dimensional…

This paper presents a novel framework for nonconvex enhancement of minimization induced (MI) penalties while preserving the overall convexity of associated regularization models. MI penalties enable the adaptation to certain signal…

We study a generalization of Eulerian polynomials to the multivariate setting introduced by Br\"and\'en. Although initially these polynomials were introduced using the language of hyperbolic and stable polynomials, we manage to translate…

Many applications using large datasets require efficient methods for minimizing a proximable convex function subject to satisfying a set of linear constraints within a specified tolerance. For this task, we present a proximal projection…

Spherical localisation is a technique whose history goes back to M.Gromov and V.Milman. It's counterpart, the Euclidean localisation is extensively studied and has been put to great use in various branches of mathematics. The purpose of…

This investigation seeks to establish the practicality of numerical frame approximations. Specifically, it develops a new method to approximate the inverse frame operator and analyzes its convergence properties. It is established that…

Non-linear filtering approaches allow to obtain decompositions of images with respect to a non-classical notion of scale, induced by the choice of a convex, absolutely one-homogeneous regularizer. The associated inverse scale space flow can…

In this work, we consider the problem of minimizing the sum of Moreau envelopes of given functions, which has previously appeared in the context of meta-learning and personalized federated learning. In contrast to the existing theory that…

This paper introduces a smoothed proximal Lagrangian method for minimizing a nonconvex smooth function over a convex domain with additional explicit convex nonlinear constraints. Two key features are 1) the proposed method is single-looped,…

In this manuscript we would like to address the classical optimization problem of minimizing a proper, convex and lower semicontinuous function via the second order in time dynamics, combining viscous and Hessian-driven damping with a…

In this paper we propose optimisation methods for variational regularisation problems based on discretising the inverse scale space flow with discrete gradient methods. Inverse scale space flow generalises gradient flows by incorporating a…

The notion of a Moreau envelope is central to the analysis of first-order optimization algorithms for machine learning. Yet, it has not been developed and extended to be applied to a deep network and, more broadly, to a machine learning…

Difference of Convex (DC) optimization problems have objective functions that are differences between two convex functions. Representative ways of solving these problems are the proximal DC algorithms, which require that the convex part of…

Deep metric learning techniques have been used for visual representation in various supervised and unsupervised learning tasks through learning embeddings of samples with deep networks. However, classic approaches, which employ a fixed…

Recently, the forward-backward and Douglas-Rachford envelope functions were proposed in the literature. The stationary points of these envelope functions have a close relationship with the solutions of the possibly nonsmooth optimization…

Optimization on Riemannian manifolds widely arises in eigenvalue computation, density functional theory, Bose-Einstein condensates, low rank nearest correlation, image registration, and signal processing, etc. We propose an adaptive…

The regularized Barzilai-Borwein (RBB) method represents a promising gradient-based optimization algorithm. In this paper, by splitting the gradient into two parts and analyzing the dynamical system of difference equations governing the…

We develop a connection between mixture and envelope representations of objective functions that arise frequently in statistics. We refer to this connection using the term "hierarchical duality." Our results suggest an interesting and…

For a regularized least squares estimation of discrete-valued signals, we propose a Linearly involved Generalized Moreau Enhanced (LiGME) regularizer, as a nonconvex regularizer, of designated isolated minimizers. The proposed regularizer…