相关论文: Regularizing with Bregman-Moreau envelopes
The proximity operator of a convex function is a natural extension of the notion of a projection operator onto a convex set. This tool, which plays a central role in the analysis and the numerical solution of convex optimization problems,…
The objective of ordinal embedding is to find a Euclidean representation of a set of abstract items, using only answers to triplet comparisons of the form "Is item $i$ closer to the item $j$ or item $k$?". In recent years, numerous…
In this paper we consider minimization of a difference-of-convex (DC) function with and without linear constraints. We first study a smooth approximation of a generic DC function, termed difference-of-Moreau-envelopes (DME) smoothing, where…
We introduce the first operator splitting method for composite monotone inclusions outside of Hilbert spaces. The proposed primal-dual method constructs iteratively the best Bregman approximation to an arbitrary point from the Kuhn-Tucker…
Moreau-Yosida regularization is introduced into the framework of exact DFT. Moreau-Yosida regularization is a lossless operation on lower semicontinuous proper convex functions over separable Hilbert spaces, and when applied to the…
In this paper, we analyse a proximal method based on the idea of forward-backward splitting for sampling from distributions with densities that are not necessarily smooth. In particular, we study the non-asymptotic properties of the…
In this paper, we describe two novel changes to the Baskakov-Durrmeyer operators that improve their approximation performance. These improvements are especially designed to produce higher rates of convergence, with orders of one or two.…
We provide a simple abstract formalism of integration by parts under which we obtain some regularization lemmas. These lemmas apply to any sequence of random variables $(F_n)$ which are smooth and non-degenerated in some sense and enable…
Incorporating a non-Euclidean variable metric to first-order algorithms is known to bring enhancement. However, due to the lack of an optimal choice, such an enhancement appears significantly underestimated. In this work, we establish a…
In this work, using Moreau envelopes, we define a complete metric for the set of proper lower semicontinuous convex functions. Under this metric, the convergence of each sequence of convex functions is epi-convergence. We show that the set…
We consider structured optimisation problems defined in terms of the sum of a smooth and convex function, and a proper, l.s.c., convex (typically non-smooth) one in reflexive variable exponent Lebesgue spaces $L_{p(\cdot)}(\Omega)$. Due to…
We propose a novel Bregman descent algorithm for minimizing a convex function that is expressed as the sum of a differentiable part (defined over an open set) and a possibly nonsmooth term. The approach, referred to as the Variable Bregman…
This paper presents a detailed theoretical analysis of the three stochastic approximation proximal gradient algorithms proposed in our companion paper [49] to set regularization parameters by marginal maximum likelihood estimation. We prove…
This work introduces the class of generalized linear-quadratic functions, constructed using maximally monotone symmetric linear relations. Calculus rules and properties of the Moreau envelope for this class of functions are developed. In…
The proximal bundle method (PBM) is a fundamental and computationally effective algorithm for solving optimization problems with nonsmooth components. In this paper, we conduct a theoretical investigation of a modified proximal bundle…
We present a generalization of the proximal operator defined through a convex combination of convex objectives, where the coefficients are updated in a minimax fashion. We prove that this new operator is Bregman firmly nonexpansive with…
Convex optimization is a well-established research area with applications in almost all fields. Over the decades, multiple approaches have been proposed to solve convex programs. The development of interior-point methods allowed solving a…
We derive new explicit bounds for the total variation distance between two convolution products of $n$ probability distributions, one of which having identical convolution factors. Approximations by finite signed measures of arbitrary order…
This paper considers stochastic optimization problems with weakly convex objective and constraint functions. We propose Prox-PEP, a proximal method equipped with quadratic subproblems. To handle nonlinear equality constraints, we employ an…
Although originally designed and analyzed for convex problems, the alternating direction method of multipliers (ADMM) and its close relatives, Douglas-Rachford splitting (DRS) and Peaceman-Rachford splitting (PRS), have been observed to…