Related papers: Inertial Proximal Incremental Aggregated Gradient …
In this paper we analyze several inexact fast augmented Lagrangian methods for solving linearly constrained convex optimization problems. Mainly, our methods rely on the combination of excessive-gap-like smoothing technique developed in…
An efficient proximal-gradient-based method, called proximal extrapolated gradient method, is designed for solving monotone variational inequality in Hilbert space. The proposed method extends the acceptable range of parameters to obtain…
In this work, we present and analyze C-SAGA, a (deterministic) cyclic variant of SAGA. C-SAGA is an incremental gradient method that minimizes a sum of differentiable convex functions by cyclically accessing their gradients. Even though the…
The proximal gradient algorithm has been popularly used for convex optimization. Recently, it has also been extended for nonconvex problems, and the current state-of-the-art is the nonmonotone accelerated proximal gradient algorithm.…
We address composite optimization problems, which consist in minimizing the sum of a smooth and a merely lower semicontinuous function, without any convexity assumptions. Numerical solutions of these problems can be obtained by proximal…
Accelerated proximal gradient methods have recently been developed for solving quasi-static incremental problems of elastoplastic analysis with some different yield criteria. It has been demonstrated through numerical experiments that these…
Nonsmooth sparsity constrained optimization encompasses a broad spectrum of applications in machine learning. This problem is generally non-convex and NP-hard. Existing solutions to this problem exhibit several notable limitations,…
The Fast Proximal Gradient Method (FPGM) and the Monotone FPGM (MFPGM) for minimization of nonsmooth convex functions are introduced and applied to tomographic image reconstruction. Convergence properties of the sequence of objective…
This paper addresses the bilinearly coupled minimax optimization problem: $\min_{x \in \mathbb{R}^{d_x}}\max_{y \in \mathbb{R}^{d_y}} \ f_1(x) + f_2(x) + y^{\top} Bx - g_1(y) - g_2(y)$, where $f_1$ and $g_1$ are smooth convex functions,…
The incremental gradient method is a prominent algorithm for minimizing a finite sum of smooth convex functions, used in many contexts including large-scale data processing applications and distributed optimization over networks. It is a…
We consider the exact continuous relaxation model of matrix rank minimization problem proposed by Yu and Zhang (Comput.Optim.Appl. 1-20, 2022). Motivated by the inertial techinique, we propose a general inertial smoothing proximal gradient…
We analyze the convergence rate of a family of inertial algorithms, which can be obtained by discretization of an inertial system with Hessian-driven damping. We recover a convergence rate, up to a factor of 2 speedup upon Nesterov's…
We consider the problem of minimizing the sum of an average function of a large number of smooth convex components and a general, possibly non-differentiable, convex function. Although many methods have been proposed to solve this problem…
We consider structured minimization problems subject to smooth inequality constraints and present a flexible algorithm that combines interior point (IP) and proximal gradient schemes. While traditional IP methods cannot cope with nonsmooth…
In this paper, we propose the approximate Bregman proximal gradient algorithm (ABPG) for solving composite nonconvex optimization problems. ABPG employs a new distance that approximates the Bregman distance, making the subproblem of ABPG…
This paper presents an accelerated composite gradient (ACG) variant, referred to as the AC-ACG method, for solving nonconvex smooth composite minimization problems. As opposed to well-known ACG variants that are either based on a known…
Several decades ago the Proximal Point Algorithm (PPA) started to gain a long-lasting attraction for both abstract operator theory and numerical optimization communities. Even in modern applications, researchers still use proximal…
Many recent applications in machine learning and data fitting call for the algorithmic solution of structured smooth convex optimization problems. Although the gradient descent method is a natural choice for this task, it requires exact…
We study decentralized non-convex finite-sum minimization problems described over a network of nodes, where each node possesses a local batch of data samples. In this context, we analyze a single-timescale randomized incremental gradient…
We analyse and explain the increased generalisation performance of iterate averaging using a Gaussian process perturbation model between the true and batch risk surface on the high dimensional quadratic. We derive three phenomena…