Related papers: Understanding Nesterov's Acceleration via Proximal…

In this paper, we generalize proximal methods that were originally designed for convex optimization on normed vector space to non-convex pose graph optimization (PGO) on special Euclidean groups, and show that our proposed generalized…

In this paper we analyze a class of nonconvex optimization problem from the viewpoint of abstract convexity. Using the respective generalizations of the subgradient we propose an abstract notion proximal operator and derive a number of…

In this paper, we propose a unified view of gradient-based algorithms for stochastic convex composite optimization by extending the concept of estimate sequence introduced by Nesterov. More precisely, we interpret a large class of…

Following the seminal work of Nesterov, accelerated optimization methods have been used to powerfully boost the performance of first-order, gradient-based parameter estimation in scenarios where second-order optimization strategies are…

Proximal methods are known to identify the underlying substructure of nonsmooth optimization problems. Even more, in many interesting situations, the output of a proximity operator comes with its structure at no additional cost, and…

In a recent study, Ansary (Optim Methods Softw 38(3):570-590,2023) proposed a Newton-type proximal gradient method for nonlinear multiobjective optimization problems (NPGMO). However, the favorable convergence properties typically…

The convergence analysis of optimization algorithms using continuous-time dynamical systems has received much attention in recent years. In this paper, we investigate applications of these systems to analyze the convergence of linearized…

Momentum based stochastic gradient methods such as heavy ball (HB) and Nesterov's accelerated gradient descent (NAG) method are widely used in practice for training deep networks and other supervised learning models, as they often provide…

In convex optimization, continuous-time counterparts have been a fruitful tool for analyzing momentum algorithms. Fewer such examples are available when the function to minimize is non-convex. In several cases, discrepancies arise between…

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…

This paper presents a majorized alternating direction method of multipliers (ADMM) with indefinite proximal terms for solving linearly constrained $2$-block convex composite optimization problems with each block in the objective being the…

We propose an adaptive smoothing algorithm based on Nesterov's smoothing technique in \cite{Nesterov2005c} for solving "fully" nonsmooth composite convex optimization problems. Our method combines both Nesterov's accelerated proximal…

Large sectors of the recent optimization literature focused in the last decade on the development of optimal stochastic first order schemes for constrained convex models under progressively relaxed assumptions. Stochastic proximal point is…

We develop a novel framework to study smooth and strongly convex optimization algorithms, both deterministic and stochastic. Focusing on quadratic functions we are able to examine optimization algorithms as a recursive application of linear…

The problem of minimizing the sum of nonsmooth, convex objective functions defined on a real Hilbert space over the intersection of fixed point sets of nonexpansive mappings, onto which the projections cannot be efficiently computed, is…

This paper develops and analyzes an online distributed proximal-gradient method (DPGM) for time-varying composite convex optimization problems. Each node of the network features a local cost that includes a smooth strongly convex function…

This paper presents a methodology and numerical algorithms for constructing accelerated gradient flows on the space of probability distributions. In particular, we extend the recent variational formulation of accelerated gradient methods in…

In sparse estimation, such as fused lasso and convex clustering, we apply either the proximal gradient method or the alternating direction method of multipliers (ADMM) to solve the problem. It takes time to include matrix division in the…

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…

We derive a second-order ordinary differential equation (ODE) which is the limit of Nesterov's accelerated gradient method. This ODE exhibits approximate equivalence to Nesterov's scheme and thus can serve as a tool for analysis. We show…