Related papers: A Variational Method for Conformable Fractional Eq…

We introduce a class of unconditionally energy stable, high order accurate schemes for gradient flows in a very general setting. The new schemes are a high order analogue of the minimizing movements approach for generating a time discrete…

The numerical solution of partial differential equations on high-dimensional domains gives rise to computationally challenging linear systems. When using standard discretization techniques, the size of the linear system grows exponentially…

We propose a new Riemannian geometry for fixed-rank matrices that is specifically tailored to the low-rank matrix completion problem. Exploiting the degree of freedom of a quotient space, we tune the metric on our search space to the…

This paper addresses the numerical solution of nonlinear eigenvector problems such as the Gross-Pitaevskii and Kohn-Sham equation arising in computational physics and chemistry. These problems characterize critical points of energy…

We consider the problem of learning low-rank tensors from partial observations with structural constraints, and propose a novel factorization of such tensors, which leads to a simpler optimization problem. The resulting problem is an…

We study the inverse problem of parameter identification in non-coercive variational problems that commonly appear in applied models. We examine the differentiability of the set-valued parameter-to-solution map by using the first-order and…

Models based on recursive adaptive partitioning such as decision trees and their ensembles are popular for high-dimensional regression as they can potentially avoid the curse of dimensionality. Because empirical risk minimization (ERM) is…

We derive the variational formulation of a gradient damage model by applying the energetic formulation of rate-independent processes and obtain a regularized formulation of fracture. The model exhibits different behavior at traction and…

Linear matrix equations, such as the Sylvester and Lyapunov equations, play an important role in various applications, including the stability analysis and dimensionality reduction of linear dynamical control systems and the solution of…

This paper interprets the stabilized finite element method via residual minimization as a variational multiscale method. We approximate the solution to the partial differential equations using two discrete spaces that we build on a…

Identifying breakpoints in piecewise regression is critical in enhancing the reliability and interpretability of data fitting. In this paper, we propose novel algorithms based on the greedy algorithm to accurately and efficiently identify…

In this paper we combine concepts from Riemannian Optimization and the theory of Sobolev gradients to derive a new conjugate gradient method for direct minimization of the Gross-Pitaevskii energy functional with rotation. The conservation…

In this paper, we propose high-order numerical methods for the Riesz space fractional advection-dispersion equations (RSFADE) on a {f}inite domain. The RSFADE is obtained from the standard advection-dispersion equation by replacing the…

We introduce a fully-corrective generalized conditional gradient method for convex minimization problems involving total variation regularization on multidimensional domains. It relies on alternatively updating an active set of subsets of…

We consider boundary value problems with Riemann-Liouville fractional derivatives of order $s\in (1, 2)$ with non-constant diffusion and reaction coefficients. A variational formulation is derived and analyzed leading to the well-posedness…

We address combinatorial problems that can be formulated as minimization of a partially separable function of discrete variables (energy minimization in graphical models, weighted constraint satisfaction, pseudo-Boolean optimization, 0-1…

The challenge of learning disentangled representation has recently attracted much attention and boils down to a competition using a new real world disentanglement dataset (Gondal et al., 2019). Various methods based on variational…

In this study, we consider the numerical solution of large systems of linear equations obtained from the stochastic Galerkin formulation of stochastic partial differential equations. We propose an iterative algorithm that exploits the…

This paper presents a modified iterative approach to solve the variational inequality problem using the double inertial technique in the context of a real Hilbert space. Our iterative technique involves a projection onto a generalized…

The goal of tensor completion is to fill in missing entries of a partially known tensor under a low-rank constraint. In this paper, we mainly study low rank third-order tensor completion problems by using Riemannian optimization methods on…