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The Alternating Direction Method of Multipliers (ADMM) is a widely used method for structured convex optimization, and its practical performance depends strongly on the choice of penalty and relaxation parameters. Motivated by settings such…
We consider solving nonconvex composite optimization problems in which the sum of a smooth function and a nonsmooth function is minimized. Many of convergence analyses of proximal gradient-type methods rely on global descent property…
Loss functions with non-isolated minima have emerged in several machine learning problems, creating a gap between theory and practice. In this paper, we formulate a new type of local convexity condition that is suitable to describe the…
We address the problem of solving convex optimization problems with many convex constraints in a distributed setting. Our approach is based on an extension of the alternating direction method of multipliers (ADMM) that recently gained a lot…
We examine the duality theory for a class of non-convex functions obtained by composing a convex function with a continuous one. Using Fenchel duality, we derive a dual problem that satisfies weak duality under general assumptions. To…
This article reports an algorithm for multi-agent distributed optimization problems with a common decision variable, local linear equality and inequality constraints and set constraints with convergence rate guarantees.…
The alternating direction method of multipliers (ADMM) is a powerful splitting algorithm for linearly constrained convex optimization problems. In view of its popularity and applicability, a growing attention is drawn towards the ADMM in…
Convex optimization has become ubiquitous in most quantitative disciplines of science, including variational image processing. Proximal splitting algorithms are becoming popular to solve such structured convex optimization problems. Within…
This paper discusses the adaptive sampling problem in a nonholonomic mobile robotic sensor network for efficiently monitoring a spatial field. It is proposed to employ Gaussian process to model a spatial phenomenon and predict it at…
This paper considers decentralized optimization of convex functions with mixed affine equality constraints involving both local and global variables. Constraints on global variables may vary across different nodes in the network, while…
Large-scale constrained optimization is pivotal in modern scientific, engineering, and industrial computation, often involving complex systems with numerous variables and constraints. This paper provides a unified and comprehensive…
This paper aims to present a fairly accessible generalization of several symmetric Gauss-Seidel decomposition based multi-block proximal alternating direction methods of multipliers (ADMMs) for convex composite optimization problems. The…
Alternating direction method of multipliers (ADMM) is a popular first-order method owing to its simplicity and efficiency. However, similar to other proximal splitting methods, the performance of ADMM degrades significantly when the scale…
The alternating direction method of multipliers (ADMM) has been widely used for solving structured convex optimization problems. In particular, the ADMM can solve convex programs that minimize the sum of $N$ convex functions with $N$-block…
Douglas-Rachford splitting and its equivalent dual formulation ADMM are widely used iterative methods in composite optimization problems arising in control and machine learning applications. The performance of these algorithms depends on…
We give a general proof of convergence for the Alternating Direction Method of Multipliers (ADMM). ADMM is an optimization algorithm that has recently become very popular due to its capabilities to solve large-scale and/or distributed…
We consider projection algorithms for solving (nonconvex) feasibility problems in Euclidean spaces. Of special interest are the Method of Alternating Projections (MAP) and the Douglas-Rachford or Averaged Alternating Reflection Algorithm…
The alternating direction method of multipliers (ADMM) proposed by Glowinski and Marrocco is a benchmark algorithm for two-block separable convex optimization problems with linear equality constraints. It has been modified, specified, and…
We propose a new relative-error inexact version of the alternating direction method of multipliers (ADMM) for convex optimization. We prove the asymptotic convergence of our main algorithm as well as pointwise and ergodic…
This paper focuses on investigating an inexact stochastic model-based optimization algorithm that integrates preconditioning techniques for solving stochastic composite optimization problems. The proposed framework unifies and extends the…