相关论文: A modified generalized shift-splitting preconditio…

We propose and analyze a general framework called nonlinear preconditioned primal-dual with projection for solving nonconvex-nonconcave and non-smooth saddle-point problems. The framework consists of two steps. The first is a nonlinear…

We propose a Multi-step Screening Procedure (MSP) for the recovery of sparse linear models in high-dimensional data. This method is based on a repeated small penalty strategy that quickly converges to an estimate within a few iterations.…

We present a scalable approach to solve a class of elliptic partial differential equation (PDE)-constrained optimization problems with bound constraints. This approach utilizes a robust full-space interior-point (IP)-Gauss-Newton…

We consider effective preconditioners for solving Laplacians of general weighted graphs. Theoretically, spectral sparsifiers (SSs) provide preconditioners of optimal computational complexity. However, they are not easy to use for real-world…

Inference in models where the parameter is defined by moment inequalities is of interest in many areas of economics. This paper develops a new method for improving the performance of generalized moment selection (GMS) testing procedures in…

We propose an inexact Uzawa algorithm with two variable relaxation parameters for solving the generalized saddle-point system. The saddle-point problems can be found in a wide class of applications, such as the augmented Lagrangian…

This work is inspired by the problem of planning sequences of operations, as welding, in car manufacturing stations where multiple industrial robots cooperate. The goal is to minimize the station cycle time, \emph{i.e.} the time it takes…

This paper proposes and analyzes a dampened proximal alternating direction method of multipliers (DP.ADMM) for solving linearly-constrained nonconvex optimization problems where the smooth part of the objective function is nonseparable.…

This paper studies the solution of nonsymmetric linear systems by preconditioned Krylov methods based on the normal equations, LSQR in particular. On some examples, preconditioned LSQR is seen to produce errors many orders of magnitude…

We consider (stochastic) convex-concave saddle point (SP) problems with high-dimensional decision variables, arising in various applications including machine learning problems. To contend with the challenges in computing full gradients, we…

Generalized Sliced Inverse Regression (GSIR) is one of the most important methods for nonlinear sufficient dimension reduction. As shown in Li and Song (2017), it enjoys a convergence rate that is independent of the dimension of the…

The solution of systems of linear(ized) equations lies at the heart of many problems in Scientific Computing. In particular for systems of large dimension, iterative methods are a primary approach. Stationary iterative methods are generally…

This work considers the convergence of GMRES for non-singular problems. GMRES is interpreted as the GCR method which allows for simple proofs of the convergence estimates. Preconditioning and weighted norms within GMRES are considered. The…

We study the performance of a new block preconditioner for a class of $3\times3$ block saddle point problems which arise from finite element methods for solving time-dependent Maxwell equations and some other practical problems. We also…

Hardware trends have motivated the development of mixed precision algo-rithms in numerical linear algebra, which aim to decrease runtime while maintaining acceptable accuracy. One recent development is the development of an adaptive…

{In [X. L. Lin, M. K. Ng, and Y. Zhi. {\it J. Comput. Phys.}, 434 (2021), pp. 110221] and [Y. L. Zhao, J. Wu, X. M. Gu, and H. Li. {\it Comput. Math. Appl.}, 148(2023), pp. 200--210]}, two-sided preconditioning techniques are proposed for…

The preconditioned iterative solution of large-scale saddle-point systems is of great importance in numerous application areas, many of them involving partial differential equations. Robustness with respect to certain problem parameters is…

Neumann series underlie both Krylov methods and algebraic multigrid smoothers. A low-synch modified Gram-Schmidt (MGS)-GMRES algorithm is described that employs a Neumann series to accelerate the projection step. A corollary to the backward…

In this paper, to solve a broad class of complex symmetric linear systems, we recast the complex system in a real formulation and apply the generalized successive overrelaxation (GSOR) iterative method to the equivalent real system. We then…

We present GraSSP, a novel approach to perform automated parallelization relying on recent advances in formal verification and synthesis. GraSSP augments an existing sequential program with an additional functionality to decompose data…