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The paper presents primal-dual proximal splitting methods for convex optimization, in which generalized Bregman distances are used to define the primal and dual proximal update steps. The methods extend the primal and dual Condat-Vu…

Optimization and Control · Mathematics 2024-08-20 Xin Jiang , Lieven Vandenberghe

We consider the scenario of classical communication over a finite-dimensional quantum channel with memory using a separable-state input ensemble and local output measurements. We propose algorithms for estimating the information rate of…

Information Theory · Computer Science 2024-10-30 Michael X. Cao , Pascal O. Vontobel

We study the convergence rate of Bregman gradient methods for convex optimization in the space of measures on a $d$-dimensional manifold. Under basic regularity assumptions, we show that the suboptimality gap at iteration $k$ is in…

Optimization and Control · Mathematics 2023-03-15 Lénaïc Chizat

Given a set of dissimilarity measurements amongst data points, determining what metric representation is most "consistent" with the input measurements or the metric that best captures the relevant geometric features of the data is a key…

Machine Learning · Computer Science 2022-09-28 Rishi Sonthalia , Anna C. Gilbert

Hybrid quantum-classical optimization using near-term quantum technology is an emerging direction for exploring quantum advantage in high-dimensional systems. However, precise characterization of all experimental parameters is often…

Quantum Physics · Physics 2019-10-11 Zhaoqi Leng , Pranav Mundada , Saeed Ghadimi , Andrew Houck

In information theory, the channel capacity, which indicates how efficient a given channel is, plays an important role. The best-used algorithm for evaluating the channel capacity is Arimoto algorithm. This paper aims to reveal an…

Information Theory · Computer Science 2022-04-04 Shoji Toyota

This paper is devoted to a new modification of a recently proposed adaptive stochastic mirror descent algorithm for constrained convex optimization problems in the case of several convex functional constraints. Algorithms, standard and its…

Optimization and Control · Mathematics 2020-01-22 Mohammad S. Alkousa

We propose a novel stochastic approximation algorithm, termed PMQSopt, for solving weakly convex stochastic optimization problems involving expectation-valued functions. The algorithm is constructed by integrating the proximal method of…

Optimization and Control · Mathematics 2026-05-06 Yule Zhang , Benqi Liu , Xiantao Xiao , Liwei Zhang

We consider a recursive algorithm to construct an aggregated estimator from a finite number of base decision rules in the classification problem. The estimator approximately minimizes a convex risk functional under the l1-constraint. It is…

Statistics Theory · Mathematics 2007-06-13 Anatoli Juditsky , Alexander Nazin , Alexandre Tsybakov , Nicolas Vayatis

Variational formulations of reconstruction in computed tomography have the notable drawback of requiring repeated evaluations of both the forward Radon transform and either its adjoint or an approximate inverse transform which are…

Numerical Analysis · Mathematics 2017-05-23 Richard C. Barnard , Rick Archibald

We present an optimized implementation of the Blahut-Arimoto algorithm via GPU parallelization, which we use to obtain improved upper bounds on the capacity of the binary deletion channel. In particular, our results imply that the capacity…

Information Theory · Computer Science 2026-04-08 Martim Pinto , João Ribeiro

We examine the last-iterate convergence rate of Bregman proximal methods - from mirror descent to mirror-prox and its optimistic variants - as a function of the local geometry induced by the prox-mapping defining the method. For generality,…

Optimization and Control · Mathematics 2024-12-13 Waïss Azizian , Franck Iutzeler , Jérôme Malick , Panayotis Mertikopoulos

The task of approximating an arbitrary convex function arises in several learning problems such as convex regression, learning with a difference of convex (DC) functions, and learning Bregman or $f$-divergences. In this paper, we develop…

The recent paper (IEEE Trans. IT 69, 1680) introduced an analytical method for calculating the channel capacity without the need for iteration. This method has certain limitations that restrict its applicability. Furthermore, the paper does…

Information Theory · Computer Science 2024-03-15 Masahito Hayashi

Near term quantum computers with a high quantity (around 50) and quality (around 0.995 fidelity for two-qubit gates) of qubits will approximately sample from certain probability distributions beyond the capabilities of known classical…

Quantum Physics · Physics 2018-01-23 Sergio Boixo , Sergei V. Isakov , Vadim N. Smelyanskiy , Hartmut Neven

Image restoration is typically addressed through non-convex inverse problems, which are often solved using first-order block-wise splitting methods. In this paper, we consider a general type of non-convex optimisation model that captures…

This paper proposes QPALM, a proximal augmented Lagrangian method based on quadratic approximations, for solving nonlinear programming problems with weakly convex objective and constraint functions. The algorithm is constructed by…

Optimization and Control · Mathematics 2026-05-06 Yule Zhang , Benqi Liu , Xiantao Xiao , Liwei Zhang

Many problems in machine learning can be formulated as optimizing a convex functional over a vector space of measures. This paper studies the convergence of the mirror descent algorithm in this infinite-dimensional setting. Defining Bregman…

Optimization and Control · Mathematics 2022-10-12 Pierre-Cyril Aubin-Frankowski , Anna Korba , Flavien Léger

In this paper, we consider an accelerated method for solving nonconvex and nonsmooth minimization problems. We propose a Bregman Proximal Gradient algorithm with extrapolation(BPGe). This algorithm extends and accelerates the Bregman…

Optimization and Control · Mathematics 2019-04-26 Xiaoya Zhang , Roberto Barrio , M. Angeles Martinez , Hao Jiang , Lizhi Cheng

We propose an iterative method for approximating the capacity of classical-quantum channels with a discrete input alphabet and a finite dimensional output, possibly under additional constraints on the input distribution. Based on duality of…

Quantum Physics · Physics 2016-01-22 David Sutter , Tobias Sutter , Peyman Mohajerin Esfahani , Renato Renner
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