Related papers: Convergence Rate of Inertial Forward-Backward Algo…

We consider forward-backward greedy algorithms for solving sparse feature selection problems with general convex smooth functions. A state-of-the-art greedy method, the Forward-Backward greedy algorithm (FoBa-obj) requires to solve a large…

Stochastic approximation (SA) is a classical approach for stochastic convex optimization. Previous studies have demonstrated that the convergence rate of SA can be improved by introducing either smoothness or strong convexity condition. In…

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],…

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…

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…

In many iterative optimization methods, fixed-point theory enables the analysis of the convergence rate via the contraction factor associated with the linear approximation of the fixed-point operator. While this factor characterizes the…

Many optimization algorithms$\unicode{x2013}$including gradient descent, proximal methods, and operator splitting techniques$\unicode{x2013}$can be formulated as fixed-point iterations (FPI) of continuous operators. When these operators are…

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…

Modern machine learning architectures are often highly expressive. They are usually over-parameterized and can interpolate the data by driving the empirical loss close to zero. We analyze the convergence of Local SGD (or FedAvg) for such…

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…

Nesterov's accelerated forward-backward algorithm (AFBA) is an efficient algorithm for solving a class of two-term convex optimization models consisting of a differentiable function with a Lipschitz continuous gradient plus a…

In this note, we consider a special instance of the scaled, inexact and adaptive generalised Fast Iterative Soft-Thresholding Algorithm (SAGE-FISTA) recently proposed in (Rebegoldi, Calatroni, '21) for the efficient solution of strongly…

Many classical and modern machine learning algorithms require solving optimization tasks under orthogonality constraints. Solving these tasks with feasible methods requires a gradient descent update followed by a retraction operation on the…

In this paper, we analyze the iteration-complexity of Generalized Forward--Backward (GFB) splitting algorithm, as proposed in \cite{gfb2011}, for minimizing a large class of composite objectives $f + \sum_{i=1}^n h_i$ on a Hilbert space,…

Error bound condition has recently gained revived interest in optimization. It has been leveraged to derive faster convergence for many popular algorithms, including subgradient methods, proximal gradient method and accelerated proximal…

Many problems in science and engineering involve, as part of their solution process, the consideration of a separable function which is the sum of two convex functions, one of them possibly non-smooth. Recently a few works have discussed…

In this paper, we derive a Fast Reflected Forward-Backward (Fast RFB) algorithm to solve the problem of finding a zero of the sum of a maximally monotone operator and a monotone and Lipschitz continuous operator in a real Hilbert space. Our…

We analyze the convergence rate of an accelerated backward forward method for solving convex composite optimization problems. The method was developed by Taylor, Hendrickx and Glineur, and is different from the FISTA algorithm in its…

Inverse problems are essential to imaging applications. In this paper, we propose a model-based deep learning network, named FISTA-Net, by combining the merits of interpretability and generality of the model-based Fast Iterative…

FISTA is a popular convex optimisation algorithm which is known to converge at an optimal rate whenever a minimiser is contained in a suitable Hilbert space. We propose a modified algorithm where each iteration is performed in a subset…