Related papers: Smooth Alternating Direction Methods for Nonsmooth…
The alternating direction method of multipliers (ADMM) is a flexible method to solve a large class of convex minimization problems. Particular features are its unconditional convergence with respect to the involved step size and its direct…
In this paper, we consider a class of nonconvex problems with linear constraints appearing frequently in the area of image processing. We solve this problem by the penalty method and propose the iteratively reweighted alternating…
This paper introduces new parameter-free first-order methods for convex optimization problems in which the objective function exhibits H\"{o}lder smoothness. Inspired by the recently proposed distance-over-gradient (DOG) technique, we…
In this paper, we propose and analyze an inexact version of the symmetric proximal alternating direction method of multipliers (ADMM) for solving linearly constrained optimization problems. Basically, the method allows its first subproblem…
In this paper, we consider the problem of minimizing the average of a large number of nonsmooth and convex functions. Such problems often arise in typical machine learning problems as empirical risk minimization, but are computationally…
In this paper, we present a generic framework that allows accelerating almost arbitrary non-accelerated deterministic and randomized algorithms for smooth convex optimization problems. The main approach of our envelope is the same as in…
In this paper, we aim to provide a comprehensive analysis on the linear rate convergence of the alternating direction method of multipliers (ADMM) for solving linearly constrained convex composite optimization problems. Under a certain…
We propose a new first-order primal-dual optimization framework for a convex optimization template with broad applications. Our optimization algorithms feature optimal convergence guarantees under a variety of common structure assumptions…
The goal of this paper is to study approaches to bridge the gap between first-order and second-order type methods for composite convex programs. Our key observations are: i) Many well-known operator splitting methods, such as…
This paper proposes a novel technique called "successive stochastic smoothing" that optimizes nonsmooth and discontinuous functions while considering various constraints. Our methodology enables local and global optimization, making it a…
Here we derive a nonsmooth maximum principle for optimal control problems with both state and mixed constraints. Crucial to our development is a convexity assumption on the "velocity set". The approach consists of applying known…
In this paper, a novel stochastic extra-step quasi-Newton method is developed to solve a class of nonsmooth nonconvex composite optimization problems. We assume that the gradient of the smooth part of the objective function can only be…
This paper presents an algorithm to solve non-convex optimal control problems, where non-convexity can arise from nonlinear dynamics, and non-convex state and control constraints. This paper assumes that the state and control constraints…
An optimization algorithm for a group of nonsmooth nonconvex problems inspired by two-stage stochastic programming problems is proposed. The main challenges for these problems include (1) the problems lack the popular lower-type properties…
Alternating direction multiplication is a powerful technique for solving convex optimisation problems. When challenging subproblems are encountered in the real world, it is useful to solve them by introducing neighbourhood terms. When the…
We consider minimization of stochastic functionals that are compositions of a (potentially) non-smooth convex function $h$ and smooth function $c$ and, more generally, stochastic weakly-convex functionals. We develop a family of stochastic…
This paper proposes a provably convergent multiblock ADMM for nonconvex optimization with nonlinear dynamics constraints, overcoming the divergence issue in classical extensions. We consider a class of optimization problems that arise from…
The paper is devoted to new modifications of recently proposed adaptive methods of Mirror Descent for convex minimization problems in the case of several convex functional constraints. Methods for problems of two classes are considered. The…
We consider a general decomposable convex optimization problem. By using right-hand side allocation technique, it can be transformed into a collection of small dimensional optimization problems. The master problem is a convex non-smooth…
This paper proposes and analyzes a communication-efficient distributed optimization framework for general nonconvex nonsmooth signal processing and machine learning problems under an asynchronous protocol. At each iteration, worker machines…