Related papers: A sparse resultant based method for efficient mini…

We propose a two-level nested preconditioned iterative scheme for solving sparse linear systems of equations in which the coefficient matrix is symmetric and indefinite with relatively small number of negative eigenvalues. The proposed…

We explore algorithms and limitations for sparse optimization problems such as sparse linear regression and robust linear regression. The goal of the sparse linear regression problem is to identify a small number of key features, while the…

We consider a discrete optimization formulation for learning sparse classifiers, where the outcome depends upon a linear combination of a small subset of features. Recent work has shown that mixed integer programming (MIP) can be used to…

Estimating covariance matrices with high-dimensional complex data presents significant challenges, particularly concerning positive definiteness, sparsity, and numerical stability. Existing robust sparse estimators often fail to guarantee…

In this paper, we propose a model's sparse representation based on reduced mixed generalized multiscale finite element (GMsFE) basis methods for elliptic PDEs with random inputs. Mixed generalized multiscale finite element method (GMsFEM)…

We propose a variant of the classical conditional gradient method for sparse inverse problems with differentiable measurement models. Such models arise in many practical problems including superresolution, time-series modeling, and matrix…

The problem of minimizing a polynomial over a set of polynomial inequalities is an NP-hard non-convex problem. Thanks to powerful results from real algebraic geometry, one can convert this problem into a nested sequence of…

Previous works have shown that reducing parameter overhead and computations for transformer-based single image super-resolution (SISR) models (e.g., SwinIR) usually leads to a reduction of performance. In this paper, we present GRFormer, an…

In this article we apply reduced order techniques for the approximation of parametric eigenvalue problems. The effect of the choice of sampling points is investigated. Here we use the standard proper orthogonal decomposition technique to…

In a plethora of applications dealing with inverse problems, e.g. in image processing, social networks, compressive sensing, biological data processing etc., the signal of interest is known to be structured in several ways at the same time.…

This paper presents a semantic planar SLAM system that improves pose estimation and mapping using cues from an instance planar segmentation network. While the mainstream approaches are using RGB-D sensors, employing a monocular camera with…

We present a new algorithm for computing a truncated Markov basis of a lattice. In general, this new algorithm is faster than existing methods. We then extend this new algorithm so that it solves the linear integer feasibility problem with…

In this paper, we propose a sparse spectral-Galerkin approximation scheme for solving the second-order partial differential equations on an arbitrary tetrahedron. Generalized Koornwinder polynomials are introduced on the reference…

We study a general class of convex submodular optimization problems with indicator variables. Many applications such as the problem of inferring Markov random fields (MRFs) with a sparsity or robustness prior can be naturally modeled in…

In this paper, we develop a (preconditioned) GMRES solver based on integer arithmetic, and introduce an iterative refinement framework for the solver. We describe the data format for the coefficient matrix and vectors for the solver that is…

We propose a gradient-based method for quadratic programming problems with a single linear constraint and bounds on the variables. Inspired by the GPCG algorithm for bound-constrained convex quadratic programming [J.J. Mor\'e and G.…

We present a class of reduced basis (RB) methods for the iterative solution of parametrized symmetric positive-definite (SPD) linear systems. The essential ingredients are a Galerkin projection of the underlying parametrized system onto a…

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…

Efficient solutions of large-scale, ill-conditioned and indefinite algebraic equations are ubiquitously needed in numerous computational fields, including multiphysics simulations, machine learning, and data science. Because of their…

We propose a stochastic variance reduced optimization algorithm for solving sparse learning problems with cardinality constraints. Sufficient conditions are provided, under which the proposed algorithm enjoys strong linear convergence…