Related papers: Distributed Solutions for Loosely Coupled Feasibil…

Convex sample approximations of chance-constrained optimization problems are considered, in which chance constraints are replaced by sets of sampled constraints. We propose a randomized sample selection strategy that allows tight bounds to…

Constrained optimization problems appear in a wide variety of challenging real-world problems, where constraints often capture the physics of the underlying system. Classic methods for solving these problems rely on iterative algorithms…

The non-smooth finite-sum minimization is a fundamental problem in machine learning. This paper develops a distributed stochastic proximal-gradient algorithm with random reshuffling to solve the finite-sum minimization over time-varying…

We consider chance-constrained problems with discrete random distribution. We aim for problems with a large number of scenarios. We propose a novel method based on the stochastic gradient descent method which performs updates of the…

The Langevin algorithms are frequently used to sample the posterior distributions in Bayesian inference. In many practical problems, however, the posterior distributions often consist of non-differentiable components, posing challenges for…

Splitting methods have emerged as powerful tools to address complex problems by decomposing them into smaller solvable components. In this work, we develop a general approach to forward-backward splitting methods for solving monotone…

A fundamental problem arising in many areas of machine learning is the evaluation of the likelihood of a given observation under different nominal distributions. Frequently, these nominal distributions are themselves estimated from data,…

In this paper we consider a distributed optimization scenario in which the aggregate objective function to minimize is partitioned, big-data and possibly non-convex. Specifically, we focus on a set-up in which the dimension of the decision…

In this paper, we propose new sequential randomized algorithms for convex optimization problems in the presence of uncertainty. A rigorous analysis of the theoretical properties of the solutions obtained by these algorithms, for full…

We propose a novel probabilistic approach to multilevel clustering problems based on composite transportation distance, which is a variant of transportation distance where the underlying metric is Kullback-Leibler divergence. Our method…

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…

This paper proposes a mechanism to fine-tune convex approximations of probabilistic reachable sets (PRS) of uncertain dynamic systems. We consider the case of unbounded uncertainties, for which it may be impossible to find a bounded…

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…

In this paper we provide an algorithm for solving constrained composite primal-dual monotone inclusions, i.e., monotone inclusions in which a priori information on primal-dual solutions is represented via closed convex sets. The proposed…

The paper considers a split inverse problem involving component equilibrium problems in Hilbert spaces. This problem therefore is called the split equilibrium problem (SEP). It is known that almost solution methods for solving problem (SEP)…

In this paper we consider a network of processors aiming at cooperatively solving linear programming problems subject to uncertainty. Each node only knows a common cost function and its local uncertain constraint set. We propose a…

A new result in convex analysis on the calculation of proximity operators in certain scaled norms is derived. We describe efficient implementations of the proximity calculation for a useful class of functions; the implementations exploit…

The nonlinear conjugate gradient methods are known to be an effective approach for standard unconstrained optimization problems especially for large-scale problems. This paper proposes a proximal nonlinear conjugate gradient method, which…

Multi-block separable convex problems recently received considerable attention. This class of optimization problems minimizes a separable convex objective function with linear constraints. The algorithmic challenges come from the fact that…

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…