Related papers: A Unifying Framework for Variance Reduction Algori…
Composite minimization is a powerful framework in large-scale convex optimization, based on decoupling of the objective function into terms with structurally different properties and allowing for more flexible algorithmic design. We…
We give in this paper a convergence result concerning parallel asynchronous algorithm with bounded delays to solve a nonlinear fixed point problems. This result is applied to calculate the solution of a strongly monotone operator. Special…
We develop a novel optimistic gradient-type algorithmic framework, combining both Nesterov's acceleration and variance-reduction techniques, to solve a class of generalized equations involving possibly nonmonotone operators in data-driven…
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…
We propose stochastic splitting algorithms for solving large-scale composite inclusion problems involving monotone and linear operators. They activate at each iteration blocks of randomly selected resolvents of monotone operators and,…
We address the problem of finding the zeros of the sum of a maximally monotone operator and a cocoercive operator. Our approach introduces a modification to the forward-backward method by integrating an inertial/momentum term alongside a…
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…
Variational inequalities are a universal optimization paradigm that is interesting in itself, but also incorporates classical minimization and saddle point problems. Modern realities encourage to consider stochastic formulations of…
The convergence of a new general variable metric algorithm based on compositions of averaged operators is established. Applications to monotone operator splitting are presented.
We consider the Frank-Wolfe algorithm for solving variational inequalities over compact, convex sets under a monotone $C^1$ operator and vanishing, nonsummable step sizes. We introduce a continuous-time interpolation of the discrete…
In this work, we propose and analyse forward-backward-type algorithms for finding a zero of the sum of finitely many monotone operators, which are not based on reduction to a two operator inclusion in the product space. Each iteration of…
In this paper we are concerned with solving monotone inclusion problems expressed by the sum of a set-valued maximally monotone operator with a single-valued maximally monotone one and the normal cone to the nonempty set of zeros of another…
In this paper we investigate the convergence behavior of a primal-dual splitting method for solving monotone inclusions involving mixtures of composite, Lipschitzian and parallel sum type operators proposed by Combettes and Pesquet in [7].…
We present a family of distributed forward-backward methods with variable stepsizes to find a solution of structured monotone inclusion problems. The framework is constructed by means of relocated fixed-point iterations, extending the…
We introduce a relaxed inertial forward-backward-forward (RIFBF) splitting algorithm for approaching the set of zeros of the sum of a maximally monotone operator and a single-valued monotone and Lipschitz continuous operator. This work aims…
The deviation vectors provide additional degrees of freedom and effectively enhance the flexibility of algorithms. In the literature, the iterative schemes with deviations are constructed and their convergence analyses are performed on an…
We introduce and study the convergence properties of a projection-type algorithm for solving the variational inequality problem for point-to-set operators. No monotoni\-city assumption is used in our analysis. The operator defining the…
We study nested variational inequalities, which are variational inequalities whose feasible set is the solution set of another variational inequality. We present a projected averaging Tikhonov algorithm requiring the weakest conditions in…
We study a class of nonconvex nonsmooth optimization problems in which the objective is a sum of two functions: One function is the average of a large number of differentiable functions, while the other function is proper, lower…
We propose a two-phase systematical framework for approximation algorithm design and analysis via Lyapunov function. The first phase consists of using Lyapunov function as an input and outputs a continuous-time approximation algorithm with…