Related papers: "FISTA" in Banach spaces with adaptive discretisat…
In [19], a general, inexact, efficient proximal quasi-Newton algorithm for composite optimization problems has been proposed and a sublinear global convergence rate has been established. In this paper, we analyze the convergence properties…
We study $\ell^1$ regularized least squares optimization problem in a separable Hilbert space. We show that the iterative soft-thresholding algorithm (ISTA) converges linearly, without making any assumption on the linear operator into play…
A problem of great interest in optimization is to minimize a sum of two closed, proper, and convex functions where one is smooth and the other has a computationally inexpensive proximal operator. In this paper we analyze a family of…
This paper presents a multilevel framework for inertial and inexact proximal algorithms, that encompasses multilevel versions of classical algorithms such as forward-backward and FISTA. The methods are supported by strong theoretical…
Non-differentiable and constrained optimization play a key role in machine learning, signal and image processing, communications, and beyond. For high-dimensional minimization problems involving large datasets or many unknowns, the…
In this paper, we propose a new algorithm to speed-up the convergence of accelerated proximal gradient (APG) methods. In order to minimize a convex function $f(\mathbf{x})$, our algorithm introduces a simple line search step after each…
In October 2025, research by Bo\c{t}, Fadili, and Nguyen, and by Jang and Ryu, led to the seminal result that Beck and Teboulle's FISTA converges weakly to a minimizer of the sum of two convex functions resolving a long-standing open…
Solving inverse problems with iterative algorithms is popular, especially for large data. Due to time constraints, the number of possible iterations is usually limited, potentially affecting the achievable accuracy. Given an error one is…
The most popular first-order accelerated black-box methods for solving large-scale convex optimization problems are the Fast Gradient Method (FGM) and the Fast Iterative Shrinkage Thresholding Algorithm (FISTA). FGM requires that the…
Targeted data selection has emerged as a crucial paradigm for efficient instruction tuning, aiming to identify a small yet influential subset of training examples for a specific target task. In practice, influence is often measured through…
In this paper, we describe a novel iterative procedure called SISTA to learn the underlying cost in optimal transport problems. SISTA is a hybrid between two classical methods, coordinate descent ("S"-inkhorn) and proximal gradient descent…
It is well-established that many iterative sparse reconstruction algorithms can be unrolled to yield a learnable neural network for improved empirical performance. A prime example is learned ISTA (LISTA) where weights, step sizes and…
We consider a class of assortment optimization problems in an offline data-driven setting. A firm does not know the underlying customer choice model but has access to an offline dataset consisting of the historically offered assortment set,…
The design of novel algorithms for solving inverse problems in signal processing is an incredibly difficult, heuristic-driven, and time-consuming task. In this short paper, we the idea of automated algorithm discovery in the signal…
In this paper, we consider a class of Forward--Backward (FB) splitting methods that includes several variants (e.g. inertial schemes, FISTA) for minimizing the sum of two proper convex and lower semi-continuous functions, one of which has a…
For first-order smooth optimization, the research on the acceleration phenomenon has a long-time history. Until recently, the mechanism leading to acceleration was not successfully uncovered by the gradient correction term and its…
Recent advances in convex optimization have leveraged computer-assisted proofs to develop optimized first-order methods that improve over classical algorithms. However, each optimized method is specially tailored for a particular problem…
Beck and Teboulle's FISTA for finding the minimizer of the sum of two convex functions is one of the most important algorithms of the past decades. While function value convergence of the iterates was known, the actual convergence of the…
The linear inverse problem emerges from various real-world applications such as Image deblurring, inpainting, etc., which are still thrust research areas for image quality improvement. In this paper, we have introduced a new algorithm…
When considering the minimization of a quadratic or strongly convex function, it is well known that first-order methods involving an inertial term weighted by a constant-in-time parameter are particularly efficient (see Polyak [32],…