Related papers: Online Primal-Dual Algorithms with Configuration L…

Applications involving dictionary learning, non-negative matrix factorization, subspace clustering, and parallel factor tensor decomposition tasks motivate well algorithms for per-block-convex and non-smooth optimization problems. By…

In this paper we study nonconvex and nonsmooth multi-block optimization over Riemannian manifolds with coupled linear constraints. Such optimization problems naturally arise from machine learning, statistical learning, compressive sensing,…

Nonconvex-nonconcave minimax optimization has gained widespread interest over the last decade. However, most existing works focus on variants of gradient descent-ascent (GDA) algorithms, which are only applicable to smooth nonconvex-concave…

In this paper we investigate the convergence of a recently popular class of first-order primal-dual algorithms for saddle point problems under the presence of errors occurring in the proximal maps and gradients. We study several types of…

Stochastic approximation techniques have been used in various contexts in data science. We propose a stochastic version of the forward-backward algorithm for minimizing the sum of two convex functions, one of which is not necessarily…

The usual approach to developing and analyzing first-order methods for smooth convex optimization assumes that the gradient of the objective function is uniformly smooth with some Lipschitz constant $L$. However, in many settings the…

In this paper, we suggest a new framework for analyzing primal subgradient methods for nonsmooth convex optimization problems. We show that the classical step-size rules, based on normalization of subgradient, or on the knowledge of optimal…

Motivated by energy management for micro-grids, we study convex optimization problems with uncertainty in the objective function and sequential decision making. To solve these problems, we propose a new framework called ``Online…

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…

We study geometric duality for convex vector optimization problems. For a primal problem with a $q$-dimensional objective space, we formulate a dual problem with a $(q+1)$-dimensional objective space. Consequently, different from an…

We study online convex optimization in the random order model, recently proposed by \citet{garber2020online}, where the loss functions may be chosen by an adversary, but are then presented to the online algorithm in a uniformly random…

Learning-augmented algorithms have been extensively studied across the computer science community in the recent years, driven by advances in machine learning predictors, which can provide additional information to augment classical…

In this paper, we study the local linear convergence properties of a versatile class of Primal-Dual splitting methods for minimizing composite non-smooth convex optimization problems. Under the assumption that the non-smooth components of…

Many realistic decision-making problems in networked scenarios, such as formation control and collaborative task offloading, often involve complicatedly entangled local decisions, which, however, have not been sufficiently investigated yet.…

This paper proposes a primal-dual framework to learn a stable estimator for linear constrained estimation problems leveraging the moving horizon approach. To avoid the online computational burden in most existing methods, we learn a…

We consider the following scheduling problem. There is a single machine and the jobs will arrive for completion online. Each job j is preemptive and, upon its arrival, its other characteristics are immediately revealed to the machine: the…

This paper proposes a novel family of primal-dual-based distributed algorithms for smooth, convex, multi-agent optimization over networks that uses only gradient information and gossip communications. The algorithms can also employ…

We study online combinatorial auctions with production costs proposed by Blum et al. using the online primal dual framework. In this model, buyers arrive online, and the seller can produce multiple copies of each item subject to a…

We investigate the distributed multi-agent sharing optimization problem in a directed graph, with a composite objective function consisting of a smooth function plus a convex (possibly non-smooth) function shared by all agents. While…

Mehta and Panigrahi (FOCS 2012) introduce the problem of online matching with stochastic rewards, where edges are associated with success probabilities and a match succeeds with the probability of the corresponding edge. It is one of the…