Related papers: Proximal algorithms for large-scale statistical mo…

This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…

We present new algorithms and fast implementations to find efficient approximations for modelling stochastic processes. For many numerical computations it is essential to develop finite approximations for stochastic processes. While the…

We address the design and synthesis of optimal control strategies for high-dimensional stochastic dynamical systems. Such systems may be deterministic nonlinear systems evolving from random initial states, or systems driven by random…

In this paper we develop proximal methods for statistical learning. Proximal point algorithms are useful in statistics and machine learning for obtaining optimization solutions for composite functions. Our approach exploits closed-form…

This paper focuses on stochastic proximal gradient methods for optimizing a smooth non-convex loss function with a non-smooth non-convex regularizer and convex constraints. To the best of our knowledge we present the first non-asymptotic…

In contrast with many other convex optimization classes, state-of-the-art semidefinite programming solvers are yet unable to efficiently solve large scale instances. This work aims to reduce this scalability gap by proposing a novel…

Decentralized optimization is a powerful paradigm that finds applications in engineering and learning design. This work studies decentralized composite optimization problems with non-smooth regularization terms. Most existing gradient-based…

Advances in numerical optimization have supported breakthroughs in several areas of signal processing. This paper focuses on the recent enhanced variants of the proximal gradient numerical optimization algorithm, which combine quasi-Newton…

We consider large linear and nonlinear fixed point problems, and solution with proximal algorithms. We show that there is a close connection between two seemingly different types of methods from distinct fields: 1) Proximal iterations for…

Majorization-minimization algorithms consist of iteratively minimizing a majorizing surrogate of an objective function. Because of its simplicity and its wide applicability, this principle has been very popular in statistics and in signal…

Convex nonsmooth optimization problems, whose solutions live in very high dimensional spaces, have become ubiquitous. To solve them, the class of first-order algorithms known as proximal splitting algorithms is particularly adequate: they…

Many applications in machine learning or signal processing involve nonsmooth optimization problems. This nonsmoothness brings a low-dimensional structure to the optimal solutions. In this paper, we propose a randomized proximal gradient…

Dual control explicitly addresses the problem of trading off active exploration and exploitation in the optimal control of partially unknown systems. While the problem can be cast in the framework of stochastic dynamic programming, exact…

We provide a unifying framework for distributed convex optimization over time-varying networks, in the presence of constraints and uncertainty, features that are typically treated separately in the literature. We adopt a proximal…

This paper proposes a novel proximal-gradient algorithm for a decentralized optimization problem with a composite objective containing smooth and non-smooth terms. Specifically, the smooth and nonsmooth terms are dealt with by gradient and…

Accelerated proximal gradient methods have recently been developed for solving quasi-static incremental problems of elastoplastic analysis with some different yield criteria. It has been demonstrated through numerical experiments that these…

Proximal algorithms have gained popularity in recent years in large-scale and distributed optimization problems. One such problem is the phase retrieval problem, for which proximal operators have been proposed recently. The phase retrieval…

Many large-scale and distributed optimization problems can be brought into a composite form in which the objective function is given by the sum of a smooth term and a nonsmooth regularizer. Such problems can be solved via a proximal…

Stochastic optimization lies at the core of most statistical learning models. The recent great development of stochastic algorithmic tools focused significantly onto proximal gradient iterations, in order to find an efficient approach for…

We address composite optimization problems, which consist in minimizing the sum of a smooth and a merely lower semicontinuous function, without any convexity assumptions. Numerical solutions of these problems can be obtained by proximal…