Related papers: Additive Schwarz Methods for Convex Optimization w…
We propose new restarting strategies for accelerated gradient and accelerated coordinate descent methods. Our main contribution is to show that the restarted method has a geometric rate of convergence for any restarting frequency, and so it…
In this paper, we extend the additive average Schwarz method to solve second order elliptic boundary value problems with heterogeneous coefficients inside the subdomains and across their interfaces by the mortar technique, where the mortar…
Coordinate descent methods employ random partial updates of decision variables in order to solve huge-scale convex optimization problems. In this work, we introduce new adaptive rules for the random selection of their updates. By adaptive,…
In this note we take a new look at the local convergence of alternating optimization methods for low-rank matrices and tensors. Our abstract interpretation as sequential optimization on moving subspaces yields insightful reformulations of…
The dynamic iteration method with a restricted additive Schwarz splitting is investigated to co-simulate linear differential algebraic equations system coming from RLC electrical circuit with linear components. We show the pure linear…
We develop multi-step gradient methods for network-constrained optimization of strongly convex functions with Lipschitz-continuous gradients. Given the topology of the underlying network and bounds on the Hessian of the objective function,…
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…
We propose an adaptive accelerated gradient method for solving smooth convex optimization problems. The method incorporates a scheme to determine the step size adaptively, by means of a local estimation of the smoothness constant, which is…
We study the computation of coupled advection-diffusion-reaction equations by the Schwarz waveform relaxation method. The study starts with linear equations, and it analyzes the convergence of the computation with a Dirichlet condition, a…
This article reviews recent advances in convex optimization algorithms for Big Data, which aim to reduce the computational, storage, and communications bottlenecks. We provide an overview of this emerging field, describe contemporary…
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 a new backtracking strategy based on the FISTA accelerated algorithm for multiobjective optimization problems. The strategy focuses on solving the problem of Lipschitz constant being unknown. It allows estimate parameter…
We develop two new proximal alternating penalty algorithms to solve a wide range class of constrained convex optimization problems. Our approach mainly relies on a novel combination of the classical quadratic penalty, alternating…
This paper presents a family of algorithms for decentralized convex composite problems. We consider the setting of a network of agents that cooperatively minimize a global objective function composed of a sum of local functions plus a…
Discrete optimization belongs to the set of $\mathcal{NP}$-hard problems, spanning fields such as mixed-integer programming and combinatorial optimization. A current standard approach to solving convex discrete optimization problems is the…
We propose two new alternating direction methods to solve "fully" nonsmooth constrained convex problems. Our algorithms have the best known worst-case iteration-complexity guarantee under mild assumptions for both the objective residual and…
This work proposes a novel adaptive linearized alternating direction multiplier method (LADMM) to convex optimization, which improves the convergence rate of the LADMM-based algorithm by adjusting step-size iteratively.The innovation of…
First-order methods with momentum such as Nesterov's fast gradient method are very useful for convex optimization problems, but can exhibit undesirable oscillations yielding slow convergence rates for some applications. An adaptive…
This paper is devoted to a new modification of a recently proposed adaptive stochastic mirror descent algorithm for constrained convex optimization problems in the case of several convex functional constraints. Algorithms, standard and its…
In this paper, acceleration of gradient methods for convex optimization problems with weak levels of convexity and smoothness is considered. Starting from the universal fast gradient method which was designed to be an optimal method for…