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Recent studies have shown that fractional calculus is an effective alternative mathematical tool in various scientific fields. However, some investigations indicate that results established in differential and integral calculus do not…

We introduce the Projected Push-Pull algorithm that enables multiple agents to solve a distributed constrained optimization problem with private cost functions and global constraints, in a collaborative manner. Our algorithm employs…

We investigate the vulnerabilities of consensus-based distributed optimization protocols to nodes that deviate from the prescribed update rule (e.g., due to failures or adversarial attacks). We first characterize certain fundamental…

We study distributed optimization algorithms for minimizing the average of convex functions. The applications include empirical risk minimization problems in statistical machine learning where the datasets are large and have to be stored on…

This paper proposes a distributed dual gradient tracking algorithm (DDGT) to solve resource allocation problems over an unbalanced network, where each node in the network holds a private cost function and computes the optimal resource by…

We consider the distributed optimization problem where $n$ agents each possessing a local cost function, collaboratively minimize the average of the $n$ cost functions over a connected network. Assuming stochastic gradient information is…

Most stochastic gradient tracking (GT) methods adopt pre-scheduled stepsize rules, while a few recent works studied adaptive stepsizes that attempt to respond to the problem's local landscape. These methods are typically built upon the…

Decentralized optimization to minimize a finite sum of functions over a network of nodes has been a significant focus within control and signal processing research due to its natural relevance to optimal control and signal estimation…

This paper considers the analysis of continuous time gradient-based optimization algorithms through the lens of nonlinear contraction theory. It demonstrates that in the case of a time-invariant objective, most elementary results on…

The mathematical program with equilibrium constraints (MPEC) is a powerful yet challenging class of constrained optimization problems, where the constraints are characterized by a parametrized variational inequality (VI) problem. While…

This paper studies distributed nonconvex optimization problems with stochastic gradients for a multi-agent system, in which each agent aims to minimize the sum of all agents' cost functions by using local compressed information exchange. We…

In this work, we study the classical distributed optimization problem over digraphs, where the objective function is a sum of smooth local functions. Inspired by the implicit tracking mechanism proposed in our earlier work, we develop a…

In this paper, we present a distributed algorithm for solving convex, constraint-coupled, optimization problems over peer-to-peer networks. We consider a network of processors that aim to cooperatively minimize the sum of local cost…

In this paper, we propose a novel distributed algorithm for consensus optimization over networks and a robust extension tailored to deal with asynchronous agents and packet losses. Indeed, to robustly achieve dynamic consensus on the…

The article discusses distributed gradient-descent algorithms for computing local and global minima in nonconvex optimization. For local optimization, we focus on distributed stochastic gradient descent (D-SGD)--a simple network-based…

We study diffusion and consensus based optimization of a sum of unknown convex objective functions over distributed networks. The only access to these functions is through stochastic gradient oracles, each of which is only available at a…

This paper presents a distributed continuous-time optimization framework aimed at overcoming the challenges posed by time-varying cost functions and constraints in multi-agent systems, particularly those subject to disturbances. By…

This technical note studies the distributed optimization problem of a sum of nonsmooth convex cost functions with local constraints. At first, we propose a novel distributed continuous-time projected algorithm, in which each agent knows its…

Large scale optimization problems are ubiquitous in machine learning and data analysis and there is a plethora of algorithms for solving such problems. Many of these algorithms employ sub-sampling, as a way to either speed up the…

This paper considers a distributed convex optimization problem with inequality constraints over time-varying unbalanced digraphs, where the cost function is a sum of local objectives, and each node of the graph only knows its local…