Related papers: A Second-Order Dynamical System for Solving Genera…
We develop a novel unified randomized block-coordinate primal-dual algorithm to solve a class of nonsmooth constrained convex optimization problems, which covers different existing variants and model settings from the literature. We prove…
This paper synthesizes anytime algorithms, in the form of continuous-time dynamical systems, to solve monotone variational inequalities. We introduce three algorithms that solve this problem: the projected monotone flow, the safe monotone…
In this paper, we studied the equilibrium problem where the bi-function may be quasiconvex with respect to the second variable and the feasible set is the intersection of a finite number of convex sets. We propose a projection-algorithm,…
This paper deals with a new Tikhonov regularized primal-dual dynamical system with variable mass and Hessian-driven damping for solving a convex optimization problem with linear equality constraints. The system features several…
In this paper we consider the variable inequality problem, that is, to find a solution of the inclusion given by the sum of a function and a point-to-cone application. This problem can be seen as a generalization of the classical system…
We develop a general framework for numerically solving differential equations while preserving invariants. As in standard projection methods, we project an arbitrary base integrator onto an invariant-preserving manifold, however, our method…
This paper aims at developing two versions of the generalized Newton method to compute not merely arbitrary local minimizers of nonsmooth optimization problems but just those, which possess an important stability property known as tilt…
We analyze a second-order projection method for the incompressible Navier-Stokes equations on bounded Lipschitz domains. The scheme employs a Backward Differentiation Formula of order two (BDF2) for the time discretization, combined with…
We propose in this work a subgradient extragradient method with inertial and correction terms for solving equilibrium problems in a real Hilbert space. We obtain that the sequence generated by our proposed method converges weakly to a point…
In this paper, we aim to study non-convex minimization problems via second-order (in-time) dynamics, including a non-vanishing viscous damping and a geometric Hessian-driven damping. Second-order systems that only rely on a viscous damping…
We investigate a generalized Lagrange multiplier system in a Banach space, called a mixed variational-hemivariational inequality (MVHVI, for short), which contains a hemivariational inequality and a variational inequality. First, we employ…
In this paper, a globally convergent Newton-type proximal gradient method is developed for composite multi-objective optimization problems where each objective function can be represented as the sum of a smooth function and a nonsmooth…
Cyclic block coordinate methods are a fundamental class of optimization methods widely used in practice and implemented as part of standard software packages for statistical learning. Nevertheless, their convergence is generally not well…
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 focus on nonconvex and nonsmooth minimization problems with a composite objective, where the differentiable part of the objective is freed from the usual and restrictive global Lipschitz gradient continuity assumption. This longstanding…
We develop two new proximal alternating penalty algorithms to solve a wide range class of constrained convex optimization problems. Our approach mainly relies on a novel combination of the classical quadratic penalty, alternating…
Majorization-minimization algorithms consist of successively minimizing a sequence of upper bounds of the objective function so that along the iterations the objective function decreases. Such a simple principle allows to solve a large…
We develop a dynamic generalized conditional gradient method (DGCG) for dynamic inverse problems with optimal transport regularization. We consider the framework introduced in (Bredies and Fanzon, ESAIM: M2AN, 54:2351-2382, 2020), where the…
Vector optimization problems are a generalization of multiobjective optimization in which the preference order is related to an arbitrary closed and convex cone, rather than the nonnegative octant. Due to its real life applications, it is…
When solving ill-posed inverse problems, a good choice of the prior is critical for the computation of a reasonable solution. A common approach is to include a Gaussian prior, which is defined by a mean vector and a symmetric and positive…