Related papers: Global constraints preserving SAV schemes for grad…
In this paper we present a numerical scheme for nonlinear continuity equations, which is based on the gradient flow formulation of an energy functional with respect to the quadratic transportation distance. It can be applied to a large…
Many applications of computational fluid dynamics require multiple simulations of a flow under different input conditions. In this paper, a numerical algorithm is developed to efficiently determine a set of such simulations in which the…
This paper proposes a finite element scheme, based on the Scalar Auxiliary Variable (SAV) approach, for the Cahn-Hilliard equation--a model that possesses significant physical relevance and a rich mathematical structure. A convergence…
A new formulation of the immersed boundary method, which facilitates accurate simulation of incompressible isothermal and natural convection flows around immersed bodies and which may be applied for accurate linear stability analysis of the…
Semi-Lagrangian schemes have proven to be very efficient to model advection problems. However most semi-Lagrangian schemes are not conservative. Here, a systematic method is introduced in order to enforce the conservative property on a…
A new decomposition optimization algorithm, called \textit{path-following gradient-based decomposition}, is proposed to solve separable convex optimization problems. Unlike path-following Newton methods considered in the literature, this…
This paper generalizes a previously-conceived, continuation-based optimization technique for scalar objective functions on constraint manifolds to cases of periodic and quasiperiodic solutions of delay-differential equations. A Lagrange…
In the field of global optimization, many existing algorithms face challenges posed by non-convex target functions and high computational complexity or unavailability of gradient information. These limitations, exacerbated by sensitivity to…
In the past years, augmented Lagrangian methods have been successfully applied to several classes of non-convex optimization problems, inspiring new developments in both theory and practice. In this paper we bring most of these recent…
We present high-order variational Lagrangian finite element methods for compressible fluids using a discrete energetic variational approach. Our spatial discretization is mass/momentum/energy conserving and entropy stable. Fully implicit…
This paper presents a novel stochastic gradient descent algorithm for constrained optimization. The proposed algorithm randomly samples constraints and components of the finite sum objective function and relies on a relaxed logarithmic…
We consider a general formulation of gradient flow evolution for problems whose natural framework is the one of metric spaces. The applications we deal with are concerned with the evolution of {\it capacitary measures} with respect to the…
We consider a generic decentralized constrained optimization problem over static, directed communication networks, where each agent has exclusive access to only one convex, differentiable, local objective term and one convex constraint set.…
Parametric finite element discretizations of constrained geometric flows must simultaneously address high-order geometric stiffness, mesh degeneration, and nonlinear global constraints. This paper develops a stabilized dual-SAV (scalar…
In this paper, we propose an optimally structured gradient coding scheme to mitigate the straggler problem in distributed learning. Conventional gradient coding methods often assume homogeneous straggler models or rely on excessive data…
The gradient scheme framework is based on a small number of properties and encompasses a large number of numerical methods for diffusion models. We recall these properties and develop some new generic tools associated with the gradient…
Developing high-order numerical schemes for two-phase flow in porous media that preserve key physical properties remains a significant challenge in numerical analysis. In this article, we propose a general framework to construct fully…
Despite the widespread use of gradient-based algorithms for optimizing high-dimensional non-convex functions, understanding their ability of finding good minima instead of being trapped in spurious ones remains to a large extent an open…
Gradient-based methods are widely used to solve various optimization problems, however, they are either constrained by local optima dilemmas, simple convex constraints, and continuous differentiability requirements, or limited to…
Total generalization variation (TGV) is a very powerful and important regularization for various inverse problems and computer vision tasks. In this paper, we proposed a semismooth Newton based augmented Lagrangian method to solve this…