Related papers: On subspace-constrained preconditioning for random…
There is growing awareness that errors in the model equations cannot be ignored in data assimilation methods such as four-dimensional variational assimilation (4D-Var). If allowed for, more information can be extracted from observations,…
A sequential quadratic programming method is designed for solving general smooth nonlinear stochastic optimization problems subject to expectation equality constraints. We consider the setting where the objective and constraint function…
In linear optimization, matrix structure can often be exploited algorithmically. However, beneficial presolving reductions sometimes destroy the special structure of a given problem. In this article, we discuss structure-aware…
While quantum algorithms for solving large scale systems of linear equations offer potentially exponential speedups, their application has largely been confined to sparse matrices. This work extends the scope of these algorithms to a broad…
We present a stationary iteration based upon a block splitting for a class of indefinite least squares problem. Convergence of the proposed method is investigated and optimal value of the involving parameter is used. The induced…
We are concerned with a novel Bayesian statistical framework for the characterization of natural subsurface formations, a very challenging task. Because of the large dimension of the stochastic space of the prior distribution in the…
This paper introduces inexact versions of several block-splitting preconditioners for solving the three-by-three block linear systems arising from a special class of indefinite least squares problems. We first establish the convergence…
In recent years, a myriad of advanced results have been reported in the community of imitation learning, ranging from parametric to non-parametric, probabilistic to non-probabilistic and Bayesian to frequentist approaches. Meanwhile, ample…
The randomized version of the Kaczmarz method for the solution of linear systems is known to converge linearly in expectation. In this work we extend this result and show that the recently proposed Randomized Sparse Kaczmarz method for…
Linear regression is a widely used technique to fit linear models and finds widespread applications across different areas such as machine learning and statistics. In most real-world scenarios, however, linear regression problems are often…
In this paper, we present a novel nonlinear programming-based approach to fine-tune pre-trained neural networks to improve robustness against adversarial attacks while maintaining high accuracy on clean data. Our method introduces…
We study the solution of large symmetric positive-definite linear systems in a matrix-free setting with a limited iteration budget. We focus on the preconditioned conjugate gradient (PCG) method with spectral preconditioning. Spectral…
The convergence of the conjugate gradient method for solving large-scale and sparse linear equation systems depends on the spectral properties of the system matrix, which can be improved by preconditioning. In this paper, we develop a…
We present a framework to train a structured prediction model by performing smoothing on the inference algorithm it builds upon. Smoothing overcomes the non-smoothness inherent to the maximum margin structured prediction objective, and…
A linear parameter must be consumed exactly once in the body of its function. When declaring resources such as file handles and manually managed memory as linear arguments, a linear type system can verify that these resources are used…
We present a modified version of the PRESB preconditioner for two-by-two block system of linear equations with the coefficient matrix $$\textbf{A}=\left(\begin{array}{cc} F & -G^* G & F \end{array}\right),$$ where $F\in\mathbb{C}^{n\times…
When given a generalized matrix separation problem, which aims to recover a low rank matrix $L_0$ and a sparse matrix $S_0$ from $M_0=L_0+HS_0$, the work \cite{CW25} proposes a novel convex optimization problem whose objective function is…
Inspired by prior work by Tian and by Cao and Xu, this paper presents an efficient computer-aided framework to characterize the fundamental limits of coded caching systems under the constraint of linear coding. The proposed framework…
Linear systems arise in generating samples and in calculating observables in lattice quantum chromodynamics~(QCD). Solving the Hermitian positive definite systems, which are sparse but ill-conditioned, involves using iterative methods, such…
We introduce a new general purpose multiresolution preconditioner for symmetric linear systems. Most existing multiresolution preconditioners use some standard wavelet basis that relies on knowledge of the geometry of the underlying domain.…