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Our work considers the optimization of the sum of a non-smooth convex function and a finite family of composite convex functions, each one of which is composed of a convex function and a bounded linear operator. This type of problem is…
Based on the needs of convergence proofs of preconditioned proximal point methods, we introduce notions of partial strong submonotonicity and partial (metric) subregularity of set-valued maps. We study relationships between these two…
Saddle point problems arise from many wireless applications, and primal-dual iterative algorithms are widely applied to find the saddle points. In the existing literature, the convergence results of such algorithms are established assuming…
Many problems in science and engineering involve, as part of their solution process, the consideration of a separable function which is the sum of two convex functions, one of them possibly non-smooth. Recently a few works have discussed…
In this paper we consider a distributed optimization scenario in which a set of agents has to solve a convex optimization problem with separable cost function, local constraint sets and a coupling inequality constraint. We propose a novel…
In this paper we consider a distributed optimization scenario in which a set of processors aims at cooperatively solving a class of min-max optimization problems. This set-up is motivated by peak-demand minimization problems in smart grids.…
In this work, we study resolvent splitting algorithms for solving composite monotone inclusion problems. The objective of these general problems is finding a zero in the sum of maximally monotone operators composed with linear operators.…
We consider cooperative multi-agent consensus optimization problems over an undirected network of agents, where only those agents connected by an edge can directly communicate. The objective is to minimize the sum of agent-specific…
Optimization decomposition methods are a fundamental tool to develop distributed solution algorithms for large scale optimization problems arising in fields such as machine learning and optimal control. In this paper, we present an…
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…
Image inverse problems have numerous applications, including image processing, super-resolution, and computer vision, which are important areas in image science. These application models can be seen as a three-function composite…
System performance for networks composed of interconnected subsystems can be increased if the traditionally separated subsystems are jointly optimized. Recently, parallel and distributed optimization methods have emerged as a powerful tool…
In recent years, as data and problem sizes have increased, distributed learning has become an essential tool for training high-performance models. However, the communication bottleneck, especially for high-dimensional data, is a challenge.…
This paper studies the convergence conditions and properties of the distributed adaptive signal fusion (DASF) algorithm, the framework itself having been introduced in a `Part I' companion paper. The DASF algorithm can be used to solve…
Orthogonal Frequency Division Multiplexing (OFDM) is the key component of many emerging broadband wireless access standards. The resource allocation in OFDM uplink, however, is challenging due to heterogeneity of users' Quality of Service…
Communication compression has become a key strategy to speed up distributed optimization. However, existing decentralized algorithms with compression mainly focus on compressing DGD-type algorithms. They are unsatisfactory in terms of…
This article explores distributed convex optimization with globally-coupled constraints, where the objective function is a general nonsmooth convex function, the constraints include nonlinear inequalities and affine equalities, and the…
The problem of minimizing convex functionals of probability distributions is solved under the assumption that the density of every distribution is bounded from above and below. A system of sufficient and necessary first-order optimality…
In this work, we study decentralized convex constrained optimization problems in networks. We focus on the dual averaging-based algorithmic framework that is well-documented to be superior in handling constraints and complex communication…
In many practical applications of constrained optimization, scale and solving time limits make traditional optimization solvers prohibitively slow. Thus, the research question of how to design optimization proxies -- machine learning models…