Related papers: Accelerated forward-backward and Douglas-Rachford …
Nonconvex and nonsmooth problems have recently attracted considerable attention in machine learning. However, developing efficient methods for the nonconvex and nonsmooth optimization problems with certain performance guarantee remains a…
We propose a continuous-time second-order optimization algorithm for solving unconstrained convex optimization problems with bounded Hessian. We show that this alternative algorithm has a comparable convergence rate to that of the…
The Douglas-Rachford method, a projection algorithm designed to solve continuous optimization problems, forms the basis of a useful heuristic for solving combinatorial optimization problems. In order to successfully use the method, it is…
This paper considers the problem of designing accelerated gradient-based algorithms for optimization and saddle-point problems. The class of objective functions is defined by a generalized sector condition. This class of functions contains…
We propose and analyze an Accelerated Rearrangement Method (ARM) for solving a class of nonconvex optimization problems involving two-phase composites. These problems include maximizing the (work) energy of a membrane governed by the…
The Douglas Rachford algorithm is an algorithm that converges to a minimizer of a sum of two convex functions. The algorithm consists in fixed point iterations involving computations of the proximity operators of the two functions…
This paper considers continuous-time coordination algorithms for networks of agents that seek to collectively solve a general class of nonsmooth convex optimization problems with an inherent distributed structure. Our algorithm design…
We study the convergence analysis of continuous-time dynamical systems associated with optimization methods for strongly convex functions. Recent works have proposed systematic constructions of Lyapunov functions for such analysis, while…
The Douglas--Rachford algorithm is a classical and very successful splitting method for finding the zeros of the sums of monotone operators. When the underlying operators are normal cone operators, the algorithm solves a convex feasibility…
This paper focuses on finite-time (FT) convergent distributed algorithms for solving time-varying (TV) distributed optimization (TVDO). The objective is to minimize the sum of local TV cost functions subject to the possible TV constraints…
By enabling the nodes or agents to solve small-sized subproblems to achieve coordination, distributed algorithms are favored by many networked systems for efficient and scalable computation. While for convex problems, substantial…
We propose a forward-backward splitting dynamical system for solving inclusion problems of the form $0\in A(x)+B(x)$ in Hilbert spaces, where $A$ is a maximal operator and $B$ is a single-valued operator. Involved operators are assumed to…
We analyze a modified version of Nesterov accelerated gradient algorithm, which applies to affine fixed point problems with non self-adjoint matrices, such as the ones appearing in the theory of Markov decision processes with discounted or…
This paper investigates the weighted-averaging dynamic for unconstrained and constrained consensus problems. Through the use of a suitably defined adjoint dynamic, quadratic Lyapunov comparison functions are constructed to analyze the…
In this paper, we propose in a Hilbertian setting a second-order time-continuous dynamic system with fast convergence guarantees to solve structured convex minimization problems with an affine constraint. The system is associated with 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…
This paper provides a theoretical and numerical comparison of classical first-order splitting methods for solving smooth convex optimization problems and cocoercive equations. From a theoretical point of view, we compare convergence rates…
Forward-backward methods are a very useful tool for the minimization of a functional given by the sum of a differentiable term and a nondifferentiable one and their investigation has experienced several efforts from many researchers in the…
We study the variable metric forward-backward splitting algorithm for convex minimization problems without the standard assumption of the Lipschitz continuity of the gradient. In this setting, we prove that, by requiring only mild…
We study the trade-offs between convergence rate and robustness to gradient errors in designing a first-order algorithm. We focus on gradient descent (GD) and accelerated gradient (AG) methods for minimizing strongly convex functions when…