相关论文: Primal-Dual Rates and Certificates

In this paper we propose distributed dual gradient algorithms for linearly constrained separable convex problems and analyze their rate of convergence under different assumptions. Under the strong convexity assumption on the primal…

In this work, we show that for linearly constrained optimization problems the primal-dual hybrid gradient algorithm, analyzed by Chambolle and Pock [3], can be written as an entirely primal algorithm. This allows us to prove convergence of…

The paper studies a distributed constrained optimization problem, where multiple agents connected in a network collectively minimize the sum of individual objective functions subject to a global constraint being an intersection of the local…

This paper develops a general theoretical framework to analyze structured sparse recovery problems using the notation of dual certificate. Although certain aspects of the dual certificate idea have already been used in some previous work,…

Best subset selection is considered the `gold standard' for many sparse learning problems. A variety of optimization techniques have been proposed to attack this non-convex and NP-hard problem. In this paper, we investigate the dual forms…

There is a recent interest on first-order methods for linear programming (LP). In this paper,we propose a stochastic algorithm using variance reduction and restarts for solving sharp primal-dual problems such as LP. We show that the…

Accuracy certificates for convex minimization problems allow for online verification of the accuracy of approximate solutions and provide a theoretically valid online stopping criterion. When solving the Lagrange dual problem, accuracy…

We propose primal-dual stochastic mirror descent for the convex optimization problems with functional constraints. We obtain the rate of convergence in terms of probability of large deviations.

We develop a novel primal-dual algorithm to solve a class of nonsmooth and nonlinear compositional convex minimization problems, which covers many existing and brand-new models as special cases. Our approach relies on a combination of a new…

In this paper we propose a distributed dual gradient algorithm for minimizing linearly constrained separable convex problems and analyze its rate of convergence. In particular, we prove that under the assumption of strong convexity and…

Primal-dual methods for solving convex optimization problems with functional constraints often exhibit a distinct two-stage behavior. Initially, they converge towards a solution at a sublinear rate. Then, after a certain point, the method…

By exploiting double-penalty terms for the primal subproblem, we develop a novel relaxed augmented Lagrangian method for solving a family of convex optimization problems subject to equality or inequality constraints. The method is then…

Given a convex optimization problem and its dual, there are many possible first-order algorithms. In this paper, we show the equivalence between mirror descent algorithms and algorithms generalizing the conditional gradient method. This is…

The domain of online algorithms with predictions has been extensively studied for different applications such as scheduling, caching (paging), clustering, ski rental, etc. Recently, Bamas et al., aiming for an unified method, have provided…

We consider a primal-dual algorithm for minimizing $f(x)+h\square l(Ax)$ with Fr\'echet differentiable $f$ and $l^*$. This primal-dual algorithm has two names in literature: Primal-Dual Fixed-Point algorithm based on the Proximity Operator…

We propose a scalable, efficient and statistically motivated computational framework for Graphical Lasso (Friedman et al., 2007b) - a covariance regularization framework that has received significant attention in the statistics community…

Screening rules allow to early discard irrelevant variables from the optimization in Lasso problems, or its derivatives, making solvers faster. In this paper, we propose new versions of the so-called $\textit{safe rules}$ for the Lasso.…

We develop a unified theory of augmented Lagrangians for nonconvex optimization problems that encompasses both duality theory and convergence analysis of primal-dual augmented Lagrangian methods in the infinite dimensional setting. Our goal…

Conventional image reconstruction models for lensless cameras often assume that each measurement results from convolving a given scene with a single experimentally measured point-spread function. These image reconstruction models fall short…

This paper introduces a novel approach to contextual stochastic optimization, integrating operations research and machine learning to address decision-making under uncertainty. Traditional methods often fail to leverage contextual…