Related papers: A General Mixed-Order Primal-Dual Dynamical System…
In this work, we approach the minimization of a continuously differentiable convex function under linear equality constraints by a second-order dynamical system with an asymptotically vanishing damping term. The system under consideration…
We study Tikhonov regularization for certain classes of non-linear ill-posed operator equations in Hilbert space. Emphasis is on the case where the solution smoothness fails to have a finite penalty value, as in the preceding study…
This paper is devoted to the study of acceleration methods for an inequality constrained convex optimization problem by using Lyapunov functions. We first approximate such a problem as an unconstrained optimization problem by employing the…
This work is concerned with the efficient optimization method for solving a large class of optimal mass transport problems. An inexact primal-dual algorithm is presented from the time discretization of a proper dynamical system, and by…
We consider primal-dual mixed finite element methods for the solution of the elliptic Cauchy problem, or other related data assimilation problems. The method has a local conservation property. We derive a priori error estimates using known…
First order optimization algorithms play a major role in large scale machine learning. A new class of methods, called adaptive algorithms, were recently introduced to adjust iteratively the learning rate for each coordinate. Despite great…
We study the problem of minimizing a sum of local objective convex functions over a network of processors/agents. This problem naturally calls for distributed optimization algorithms, in which the agents cooperatively solve the problem…
We investigate the strong convergence properties of a proximal-gradient inertial algorithm with two Tikhonov regularization terms in connection to the minimization problem of the sum of a convex lower semi-continuous function $f$ and a…
In this paper, we introduce a novel Extra-Gradient method with anchor term governed by general parameters. Our method is derived from an explicit discretization of a Tikhonov-regularized monotone flow in Hilbert space, which provides a…
Previous studies on stochastic primal-dual algorithms for solving min-max problems with faster convergence heavily rely on the bilinear structure of the problem, which restricts their applicability to a narrowed range of problems. The main…
In this work, we approach the minimization of a continuously differentiable convex function under linear equality constraints by a second-order dynamical system with asymptotically vanishing damping term. The system is formulated in terms…
In a Hilbert setting we study the convergence properties of a second order in time dynamical system combining viscous and Hessian-driven damping with time scaling in relation with the minimization of a nonsmooth and convex function. The…
In a Hilbert space setting $\mathcal H$, we study the convergence properties as $t \to + \infty$ of the trajectories of the second-order differential equation \begin{equation*} \mbox{(AVD)}_{\alpha, \epsilon} \quad \quad \ddot{x}(t) +…
In this paper, based on the Tikhonov regularization technique, we study a monotone general variational inequality (GVI) by considering an associated strongly monotone GVI, depending on a regularization parameter $\alpha,$ such that the…
The problem of constrained Markov decision process (CMDP) is investigated, where an agent aims to maximize the expected accumulated discounted reward subject to multiple constraints on its utilities/costs. A new primal-dual approach is…
Continuous-time primal-dual gradient dynamics (PDGD) is an ubiquitous approach for dynamically solving constrained distributed optimization problems. Yet, the distributed nature of the dynamics makes it prone to communication uncertainties,…
We study multi-parameter regularization (multiple penalties) for solving linear inverse problems to promote simultaneously distinct features of the sought-for objects. We revisit a balancing principle for choosing regularization parameters…
In a Hilbert setting, we develop fast methods for convex unconstrained optimization. We rely on the asymptotic behavior of an inertial system combining geometric damping with temporal scaling. The convex function to minimize enters the…
We propose a third order dynamical system for solving a nonlinear equation in Hilbert spaces where the operator is cocoercive with respect to the solutions set. Under mild conditions on the parameters, we establish the existence and…
We present a novel way of generating Lyapunov functions for proving linear convergence rates of first-order optimization methods. Our approach provably obtains the fastest linear convergence rate that can be verified by a quadratic Lyapunov…