Related papers: Three Operator Splitting with a Nonconvex Loss Fun…
The obstacle problem is a class of free boundary problems which finds applications in many disciplines such as porous media, financial mathematics and optimal control. In this paper, we propose two operator-splitting methods to solve the…
In this paper, we propose a novel accelerated forward-backward splitting algorithm for minimizing convex composite functions, written as the sum of a smooth function and a (possibly) nonsmooth function. When the objective function is…
We introduce and analyze an algorithm for the minimization of convex functions that are the sum of differentiable terms and proximable terms composed with linear operators. The method builds upon the recently developed smoothed gap…
We study distributed non-convex optimization on a time-varying multi-agent network. Each node has access to its own smooth local cost function, and the collective goal is to minimize the sum of these functions. We generalize the results…
In this paper we develop a higher-order method for solving composite (non)convex minimization problems with smooth (non)convex functional constraints. At each iteration our method approximates the smooth part of the objective function and…
For a linear equality constrained convex optimization problem involving two objective functions with a ``nonsmooth" + ``nonsmooth" composite structure, we study two algorithms derived from a mixed-order dynamical system which incorporates…
This paper investigates a specific class of nonsmooth nonconvex optimization problems in the face of data uncertainty, namely, robust optimization problems, where the given objective function can be expressed as a difference of two…
The Douglas--Rachford algorithm is a classic splitting method for finding a zero of the sum of two maximal monotone operators. It has also been applied to settings that involve one weakly and one strongly monotone operator. In this work, we…
The Douglas-Rachford method is a popular splitting technique for finding a zero of the sum of two subdifferential operators of proper closed convex functions; more generally two maximally monotone operators. Recent results concerned with…
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…
We consider convex-concave saddle-point problems where the objective functions may be split in many components, and extend recent stochastic variance reduction methods (such as SVRG or SAGA) to provide the first large-scale linearly…
Our work focuses on stochastic gradient methods for optimizing a smooth non-convex loss function with a non-smooth non-convex regularizer. Research on this class of problem is quite limited, and until recently no non-asymptotic convergence…
We shed light on the structure of the "three-operator" version of the forward-Douglas--Rachford splitting algorithm for finding a zero of a sum of maximally monotone operators $A + B + C$, where $B$ is cocoercive, involving only the…
In this paper, we propose a novel Dual Inexact Splitting Algorithm (DISA) for distributed convex composite optimization problems, where the local loss function consists of a smooth term and a possibly nonsmooth term composed with a linear…
In this paper, we study a class of nonconvex and nonsmooth structured difference-of-convex (DC) programs, which contain in the convex part the sum of a nonsmooth linearly composed convex function and a differentiable function, and in the…
We develop two variance-reduced fast operator splitting methods to approximate solutions of a class of generalized equations, covering fundamental problems such as \rvs{minimization}, minimax problems, and variational inequalities as…
We study nonconvex distributed optimization in multi-agent networks with time-varying (nonsymmetric) connectivity. We introduce the first algorithmic framework for the distributed minimization of the sum of a smooth (possibly nonconvex and…
We consider convex and nonconvex constrained optimization with a partially separable objective function: agents minimize the sum of local objective functions, each of which is known only by the associated agent and depends on the variables…
We propose STARS, a randomized derivative-free algorithm for unconstrained optimization when the function evaluations are contaminated with random noise. STARS takes dynamic, noise-adjusted smoothing step-sizes that minimize the…
This paper considers computational methods that split a vector field into three components in the case when both the vector field and the split components might be unbounded. We first employ classical Taylor expansion which, after some…