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This article is devoted to one particular case of using universal accelerated proximal envelopes to obtain computationally efficient accelerated versions of methods used to solve various optimization problem setups. In this paper, we…
We introduce a generic scheme for accelerating gradient-based optimization methods in the sense of Nesterov. The approach, called Catalyst, builds upon the inexact accelerated proximal point algorithm for minimizing a convex objective…
We introduce a generic scheme for accelerating first-order optimization methods in the sense of Nesterov, which builds upon a new analysis of the accelerated proximal point algorithm. Our approach consists of minimizing a convex objective…
In this paper, we present a generic framework that allows accelerating almost arbitrary non-accelerated deterministic and randomized algorithms for smooth convex optimization problems. The main approach of our envelope is the same as in…
We propose an accelerated meta-algorithm, which allows to obtain accelerated methods for convex unconstrained minimization in different settings. As an application of the general scheme we propose nearly optimal methods for minimizing…
This paper considers the decentralized convex optimization problem, which has a wide range of applications in large-scale machine learning, sensor networks, and control theory. We propose novel algorithms that achieve optimal computation…
In this paper, we introduce various mechanisms to obtain accelerated first-order stochastic optimization algorithms when the objective function is convex or strongly convex. Specifically, we extend the Catalyst approach originally designed…
This paper proposes an accelerated proximal point method for maximally monotone operators. The proof is computer-assisted via the performance estimation problem approach. The proximal point method includes various well-known convex…
In this paper, we propose a proximal gradient method and an accelerated proximal gradient method for solving composite optimization problems, where the objective function is the sum of a smooth and a convex, possibly nonsmooth, function. We…
We analyze the convergence rate of the monotone accelerated proximal gradient method, which can be used to solve structured convex composite optimization problems. A linear convergence rate is established when the smooth part of the…
Accelerated coordinate descent is widely used in optimization due to its cheap per-iteration cost and scalability to large-scale problems. Up to a primal-dual transformation, it is also the same as accelerated stochastic gradient descent…
Despite their frequent slow convergence, proximal gradient schemes are widely used in large-scale optimization tasks due to their tremendous stability, scalability, and ease of computation. In this paper, we develop and investigate a…
In this paper, we propose new accelerated methods for smooth convex optimization, called contracting proximal methods. At every step of these methods, we need to minimize a contracted version of the objective function augmented by a…
The proximal bundle method (PBM) is a powerful and widely used approach for minimizing nonsmooth convex functions. However, for smooth objectives, its best-known convergence rate remains suboptimal, and whether PBM can be accelerated…
Composite convex optimization models arise in several applications, and are especially prevalent in inverse problems with a sparsity inducing norm and in general convex optimization with simple constraints. The most widely used algorithms…
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…
We develop a distributed algorithm for convex Empirical Risk Minimization, the problem of minimizing large but finite sum of convex functions over networks. The proposed algorithm is derived from directly discretizing the second-order…
We consider problems of minimizing functionals $\mathcal{F}$ of probability measures on the Euclidean space. To propose an accelerated gradient descent algorithm for such problems, we consider gradient flow of transport maps that give…
Decentralized optimization is well studied for smooth unconstrained problems. However, constrained problems or problems with composite terms are an open direction for research. We study structured (or composite) optimization problems, where…
In this paper, we propose a randomized accelerated method for the minimization of a strongly convex function under linear constraints. The method is of Kaczmarz-type, i.e. it only uses a single linear equation in each iteration. To obtain…