Related papers: A cut-and-project perspective for linearized Bregm…
Bilevel optimization has gained prominence in various applications. In this study, we introduce a framework for solving bilevel optimization problems, where the variables in both the lower and upper levels are constrained on Riemannian…
We discuss a special form of gradient descent that in the literature has become known as the so-called linearised Bregman iteration. The idea is to replace the classical (squared) two norm metric in the gradient descent setting with a…
Bilevel optimization is an important class of optimization problems where one optimization problem is nested within another. While various methods have emerged to address unconstrained general bilevel optimization problems, there has been a…
Many problems in machine learning write as the minimization of a sum of individual loss functions over the training examples. These functions are usually differentiable but, in some cases, their gradients are not Lipschitz continuous, which…
A typical assumption for the analysis of first order optimization methods is the Lipschitz continuity of the gradient of the objective function. However, for many practical applications this assumption is violated, including loss functions…
The training of deep neural networks predominantly relies on a combination of gradient-based optimisation and back-propagation for the computation of the gradient. While incredibly successful, this approach faces challenges such as…
Bregman divergences play a central role in the design and analysis of a range of machine learning algorithms. This paper explores the use of Bregman divergences to establish reductions between such algorithms and their analyses. We present…
Recent advancements in quantum computing and quantum-inspired algorithms have sparked renewed interest in binary optimization. These hardware and software innovations promise to revolutionize solution times for complex problems. In this…
We propose a new gradient projection algorithm that compares favorably with the fastest algorithms available to date for $\ell_1$-constrained sparse recovery from noisy data, both in the compressed sensing and inverse problem frameworks.…
We propose a version of least-mean-square (LMS) algorithm for sparse system identification. Our algorithm called online linearized Bregman iteration (OLBI) is derived from minimizing the cumulative prediction error squared along with an…
In this paper, using the Bregman distance, we introduce a new projection-type algorithm for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points. Then the strong convergence of the sequence…
This paper proposes Branch & Learn, a framework for Predict+Optimize to tackle optimization problems containing parameters that are unknown at the time of solving. Given an optimization problem solvable by a recursive algorithm satisfying…
In this paper, we propose and analyze an accelerated linearized Bregman (ALB) method for solving the basis pursuit and related sparse optimization problems. This accelerated algorithm is based on the fact that the linearized Bregman (LB)…
We study the alternating algorithm for the computation of the metric projection onto the closed sum of two closed subspaces in uniformly convex and uniformly smooth Banach spaces. For Banach spaces which are convex and smooth of power type,…
Problems in signal processing and medical imaging often lead to calculating sparse solutions to under-determined linear systems. Methodologies for solving this problem are presented as background to the method used in this work where the…
This paper studies proximal gradient iterations for solving simple bilevel optimization problems where both the upper and the lower level cost functions are split as the sum of differentiable and (possibly nonsmooth) proximable functions.…
We propose a new approach to solving bilevel optimization problems, intermediate between solving full-system optimality conditions with a Newton-type approach, and treating the inner problem as an implicit function. The overall idea is to…
Several novel mixed-integer linear and bilinear formulations are proposed for the optimum communication spanning tree problem. They implement the distance-based approach: graph distances are directly modeled by continuous, integral, or…
We study the variational inference problem of minimizing a regularized R\'enyi divergence over an exponential family. We propose to solve this problem with a Bregman proximal gradient algorithm. We propose a sampling-based algorithm to…
Channel estimation poses significant challenges in millimeter-wave massive multiple-input multiple-output systems, especially when the base station has fewer radio-frequency chains than antennas. To address this challenge, one promising…