Related papers: A Variational Method for Conformable Fractional Eq…
We present a variational reduced-order model for three-dimensional coplanar propagation of sharp cracks in heterogeneous perfectly brittle solids under mixed-mode I+II+III loading. The approach connects the variational fracture formulation…
From optimal transport to robust dimensionality reduction, a plethora of machine learning applications can be cast into the min-max optimization problems over Riemannian manifolds. Though many min-max algorithms have been analyzed in the…
Motivated by modern applications such as computerized adaptive testing, sequential rank aggregation, and heterogeneous data source selection, we study the problem of active sequential estimation, which involves adaptively selecting…
We develop an efficient stochastic variance reduced gradient descent algorithm to solve the affine rank minimization problem consists of finding a matrix of minimum rank from linear measurements. The proposed algorithm as a stochastic…
We consider the problem of minimizing a differentiable function with locally Lipschitz continuous gradient on a stratified set and present a first-order algorithm designed to find a stationary point of that problem. Our assumptions on the…
Recently, collocation based radial basis function (RBF) partition of unity methods (PUM) for solving partial differential equations have been formulated and investigated numerically and theoretically. When combined with stable evaluation…
This paper develops an enhanced finite element method for approximating a class of variational problems which exhibit the \textit{Lavrentiev gap phenomenon} in the sense that the minimum values of the energy functional have a nontrivial gap…
A finite element methodology for large classes of variational boundary value problems is defined which involves discretizing two linear operators: (1) the differential operator defining the spatial boundary value problem; and (2) a Riesz…
In this paper a new Riemannian rank adaptive method (RRAM) is proposed for the low-rank tensor completion problem (LRTCP) formulated as a least-squares optimization problem on the algebraic variety of tensors of bounded tensor-train (TT)…
This paper can be seen as an attempt of rethinking the {\em Extra-Gradient Philosophy} for solving Variational Inequality Problems. We show that the properly defined {\em Reduced Gradients} can be used instead for finding approximate…
Robust low-rank matrix completion (RMC), or robust principal component analysis with partially observed data, has been studied extensively for computer vision, signal processing and machine learning applications. This problem aims to…
Grover's algorithm is a fundamental quantum algorithm that offers a quadratic speedup for the unstructured search problem by alternately applying physically implementable oracle and diffusion operators. In this paper, we reformulate the…
In this paper, we propose a method for the approximation of the solution of high-dimensional weakly coercive problems formulated in tensor spaces using low-rank approximation formats. The method can be seen as a perturbation of a minimal…
Coordinate descent with random coordinate selection is the current state of the art for many large scale optimization problems. However, greedy selection of the steepest coordinate on smooth problems can yield convergence rates independent…
We develop computational methods for approximating the solution of a linear multi-term matrix equation in low rank. We follow an alternating minimization framework, where the solution is represented as a product of two matrices, and…
This paper is concerned with the numerical minimization of energy functionals in Hilbert spaces involving convex constraints coinciding with a semi-norm for a subspace. The optimization is realized by alternating minimizations of the…
Low rank approximation is a commonly occurring problem in many computer vision and machine learning applications. There are two common ways of optimizing the resulting models. Either the set of matrices with a given rank can be explicitly…
We present an accelerated greedy strategy for training of projection-based reduced-order models for parametric steady and unsteady partial differential equations. Our approach exploits hierarchical approximate proper orthogonal…
This paper considers an optimal radial reconfiguration problem in multi-source distribution networks, where the goal is to find a radial configuration that minimizes quadratic distribution costs while ensuring all sink demands are met. This…
Model reduction attempts to guarantee a desired "model quality", e.g. given in terms of accuracy requirements, with as small a model size as possible. This article highlights some recent developments concerning this issue for the so called…