Related papers: A Decentralized Second-Order Method with Exact Lin…
This paper presents a fully asynchronous and distributed approach for tackling optimization problems in which both the objective function and the constraints may be nonconvex. In the considered network setting each node is active upon…
This dissertation explores block decomposable methods for large-scale optimization problems. It focuses on alternating direction method of multipliers (ADMM) schemes and block coordinate descent (BCD) methods. Specifically, it introduces a…
We consider distributed nonconvex optimization over an undirected network, where each node privately possesses its local objective and communicates exclusively with its neighboring nodes, striving to collectively achieve a common optimal…
Recently, there has been significant progress in the development of distributed first order methods. (At least) two different types of methods, designed from very different perspectives, have been proposed that achieve both exact and linear…
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…
Variable selection is one of the most important tasks in statistics and machine learning. To incorporate more prior information about the regression coefficients, the constrained Lasso model has been proposed in the literature. In this…
We consider the problem of decentralized composite optimization over a symmetric connected graph, in which each node holds its own agent-specific private convex functions, and communications are only allowed between nodes with direct links.…
In this paper, we consider a network of agents that jointly aim to minimise the sum of local functions subject to coupling constraints involving all local variables. To solve this problem, we propose a novel solution based on a primal-dual…
We develop a line-search second-order algorithmic framework for minimizing finite sums. We do not make any convexity assumptions, but require the terms of the sum to be continuously differentiable and have Lipschitz-continuous gradients.…
We consider minimizing a function consisting of a quadratic term and a proximable term which is possibly nonconvex and nonsmooth. This problem is also known as scaled proximal operator. Despite its simple form, existing methods suffer from…
Augmented Lagrangian method (also called as method of multipliers) is an important and powerful optimization method for lots of smooth or nonsmooth variational problems in modern signal processing, imaging, optimal control and so on.…
Dual descent methods are commonly used to solve network flow optimization problems, since their implementation can be distributed over the network. These algorithms, however, often exhibit slow convergence rates. Approximate Newton methods…
In this paper, we study a class of convex composite optimization problems. We begin by characterizing the equivalence between the primal/dual strong second-order sufficient condition and the dual/primal nondegeneracy condition. Building on…
We introduce and study exterior distance function (EDF) and correspondent exterior point method (EPM) for convex optimization. The EDF is a classical Lagrangian for an equivalent problem obtained from the initial one by monotone…
In this paper, we propose the primal-dual method of multipliers (PDMM) for distributed optimization over a graph. In particular, we optimize a sum of convex functions defined over a graph, where every edge in the graph carries a linear…
We propose two numerical algorithms in the fully nonconvex setting for the minimization of the sum of a smooth function and the composition of a nonsmooth function with a linear operator. The iterative schemes are formulated in the spirit…
We investigate a distributed optimization problem over a cooperative multi-agent time-varying network, where each agent has its own decision variables that should be set so as to minimize its individual objective subject to local…
This paper considers consensus optimization problems where each node of a network has access to a different summand of an aggregate cost function. Nodes try to minimize the aggregate cost function, while they exchange information only with…
This paper investigates solving convex composite optimization on an undirected network, where each node, privately endowed with a smooth component function and a nonsmooth one, is required to minimize the sum of all the component functions…
We propose a communication- and computation-efficient distributed optimization algorithm using second-order information for solving empirical risk minimization (ERM) problems with a nonsmooth regularization term. Our algorithm is applicable…