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Most algorithms for solving optimization problems or finding saddle points of convex-concave functions are fixed-point algorithms. In this work we consider the generic problem of finding a fixed point of an average of operators, or an…

We consider multi-agent, convex optimization programs subject to separable constraints, where the constraint function of each agent involves only its local decision vector, while the decision vectors of all agents are coupled via a common…

This work examines the mean-square error performance of diffusion stochastic algorithms under a generalized coordinate-descent scheme. In this setting, the adaptation step by each agent is limited to a random subset of the coordinates of…

In this paper, we consider a network of processors aiming at cooperatively solving mixed-integer convex programs subject to uncertainty. Each node only knows a common cost function and its local uncertain constraint set. We propose a…

This paper explores the generalization characteristics of iterative learning algorithms with bounded updates for non-convex loss functions, employing information-theoretic techniques. Our key contribution is a novel bound for the…

We propose a unifying framework for the automated computer-assisted worst-case analysis of cyclic block coordinate algorithms in the unconstrained smooth convex optimization setup. We compute exact worst-case bounds for the cyclic…

Time-varying stochastic optimization problems frequently arise in machine learning practice (e.g. gradual domain shift, object tracking, strategic classification). Although most problems are solved in discrete time, the underlying process…

In this paper, Decentralized Periodic Approach for Adaptive Fault Diagnosis (DP-AFD) algorithm is proposed for fault diagnosis in distributed systems with arbitrary topology. Faulty nodes may be either unresponsive, may have either software…

We consider the problem of distributed optimal power flow (OPF) for multi-area electric power systems. A novel distributed algorithm is proposed, referred to as the rotated coordinate descent critical region exploration (RCDCRE). It allows…

Existing asynchronous distributed optimization algorithms often use diminishing step-sizes that cause slow practical convergence, or fixed step-sizes that depend on an assumed upper bound of delays. Not only is such a delay bound hard to…

Due to the highly non-convex nature of large-scale robust parameter estimation, avoiding poor local minima is challenging in real-world applications where input data is contaminated by a large or unknown fraction of outliers. In this paper,…

Compact finite-difference (FD) schemes specify derivative approximations implicitly, thus to achieve parallelism with domain-decomposition suitable partitioning of linear systems is required. Consistent order of accuracy, dispersion, and…

We propose an efficient distributed randomized coordinate descent method for minimizing regularized non-strongly convex loss functions. The method attains the optimal $O(1/k^2)$ convergence rate, where $k$ is the iteration counter. The core…

When optimizing real-time systems, designers often face a challenging problem where the schedulability constraints are non-convex, non-continuous, or lack an analytical form to understand their properties. Although the optimization…

We present a geometric multilevel optimization approach that smoothly incorporates box constraints. Given a box constrained optimization problem, we consider a hierarchy of models with varying discretization levels. Finer models are…

Sparse optimization is a central problem in machine learning and computer vision. However, this problem is inherently NP-hard and thus difficult to solve in general. Combinatorial search methods find the global optimal solution but are…

We consider the general problem of minimizing an objective function which is the sum of a convex function (not strictly convex) and absolute values of a subset of variables (or equivalently the l1-norm of the variables). This problem…

Leading eigenvalue problems for large scale matrices arise in many applications. Coordinate-wise descent methods are considered in this work for such problems based on a reformulation of the leading eigenvalue problem as a non-convex…

The paper studies decentralized optimization over networks, where agents minimize a composite objective consisting of the sum of smooth convex functions--the agents' losses--and an additional nonsmooth convex extended value function. We…

The circumcentered-reflection method (CRM) has been recently proposed as a methodology for accelerating several algorithms for solving the Convex Feasibility Problem (CFP), equivalent to finding a common fixed-point of the orthogonal…