Related papers: On Inexact Accelerated Proximal Gradient Methods w…
This paper provides a new way of developing the fast iterative shrinkage/thresholding algorithm (FISTA) that is widely used for minimizing composite convex functions with a nonsmooth term such as the $\ell_1$ regularizer. In particular,…
The purpose of this technical report is to review the main properties of an accelerated composite gradient (ACG) method commonly referred to as the Fast Iterative Shrinkage-Thresholding Algorithm (FISTA). In addition, we state a version of…
The "fast iterative shrinkage-thresholding algorithm", a.k.a. FISTA, is one of the most well-known first-order optimisation scheme in the literature, as it achieves the worst-case $O(1/k^2)$ optimal convergence rate in terms of objective…
This paper presents an accelerated proximal gradient method for multiobjective optimization, in which each objective function is the sum of a continuously differentiable, convex function and a closed, proper, convex function. Extending…
Fast Iterative Shrinking-Threshold Algorithm (FISTA) is a popular fast gradient descent method (FGM) in the field of large scale convex optimization problems. However, it can exhibit undesirable periodic oscillatory behaviour in some…
In this paper we propose an adaptively extrapolated proximal gradient method, which is based on the accelerated proximal gradient method (also known as FISTA), however we locally optimize the extrapolation parameter by carrying out an exact…
The ``fast iterative shrinkage-thresholding algorithm'', a.k.a. FISTA, is one of the most widely used algorithms in the literature. However, despite its optimal theoretical $O(1/k^2)$ convergence rate guarantee, oftentimes in practice its…
We present two approximate versions of the proximal subgradient method for minimizing the sum of two convex functions (not necessarily differentiable). The algorithms involve, at each iteration, inexact evaluations of the proximal operator…
Accelerated proximal gradient methods, which are also called fast iterative shrinkage-thresholding algorithms (FISTA) are known to be efficient for many applications. Recently, Tanabe et al. proposed an extension of FISTA for multiobjective…
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…
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…
We consider a variable metric and inexact version of the FISTA-type algorithm considered in (Chambolle, Pock, 2016, Calatroni, Chambolle, 2019) for the minimization of the sum of two (possibly strongly) convex functions. The proposed…
Convex-composite optimization, which minimizes an objective function represented by the sum of a differentiable function and a convex one, is widely used in machine learning and signal/image processing. Fast Iterative Shrinkage Thresholding…
In this paper, we revisit the class of iterative shrinkage-thresholding algorithms (ISTA) for solving the linear inverse problem with sparse representation, which arises in signal and image processing. It is shown in the numerical…
Introduced by Beck and Teboulle, FISTA (for Fast Iterative Shrinkage-Thresholding Algorithm) is a first-order method widely used in convex optimization. Adapted from Nesterov's accelerated gradient method for convex functions, the generated…
We consider the problem of optimizing the sum of a smooth convex function and a non-smooth convex function using proximal-gradient methods, where an error is present in the calculation of the gradient of the smooth term or in the proximity…
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…
Non-convex sparsity-inducing penalties have recently received considerable attentions in sparse learning. Recent theoretical investigations have demonstrated their superiority over the convex counterparts in several sparse learning…
In this paper, we study convex bi-level optimization problems where both the inner and outer levels are given as a composite convex minimization. We propose the Fast Bi-level Proximal Gradient (FBi-PG) algorithm, which can be interpreted as…
In this paper, we propose a novel accelerated forward-backward splitting algorithm for minimizing convex composite functions, written as the sum of a smooth function and a (possibly) nonsmooth function. When the objective function is…