Related papers: On the analysis of block smoothers for saddle poin…
The use of machine learning algorithms to address classification problems is on the rise in many research areas. The current study is aimed at testing the potential of using such algorithms to auto-select the best solvers for transport…
In practice, optimization tasks have some structure that allows developing new algorithms for every problem with faster convergence rates. Using the structure of optimization tasks, we can propose algorithms with more optimistic convergence…
This paper concerns robust numerical treatment of an elliptic PDE with high contrast coefficients, for which classical finite-element discretizations yield ill-conditioned linear systems. This paper introduces a procedure by which the…
We improve the performance of multigrid solvers on many-core architectures with cache hierarchies by reorganizing operations in the smoothing step to minimize memory transfers. We focus on patch smoothers, which offer robust convergence…
Recent focus on robustness to adversarial attacks for deep neural networks produced a large variety of algorithms for training robust models. Most of the effective algorithms involve solving the min-max optimization problem for training…
We present a robust and efficient multigrid method for single-patch isogeometric discretizations using tensor product B-splines of maximum smoothness. Our method is based on a stable splitting of the spline space into a large subspace of…
We present a practical, algebraic method for efficiently calculating the Yukawa couplings of a large class of heterotic compactifications on Calabi-Yau three-folds with non-standard embeddings. Our methodology covers all of, though is not…
We investigate three directions to further improve the highly efficient Space-Time Multigrid algorithm with block-Jacobi smoother introduced in [GanNeu16]. First, we derive an analytical expression for the optimal smoothing parameter in the…
Saddle point problems, ubiquitous in optimization, extend beyond game theory to diverse domains like power networks and reinforcement learning. This paper presents novel approaches to tackle saddle point problem, with a focus on…
In the paper, we generalize the approach Gasnikov et. al, 2017, which allows to solve (stochastic) convex optimization problems with an inexact gradient-free oracle, to the convex-concave saddle-point problem. The proposed approach works,…
We propose a new class of multi-layer iterative schemes for solving sparse linear systems in saddle point structure. The new scheme consist of an iterative preconditioner that is based on the (approximate) nullspace method, combined with an…
Most research on preconditioners for time-dependent PDEs has focused on implicit multi-step or diagonally-implicit multi-stage temporal discretizations. In this paper, we consider monolithic multigrid preconditioners for fully-implicit…
The problem of computing saddle points is important in certain problems in numerical partial differential equations and computational chemistry, and is often solved numerically by a minimization problem over a set of mountain passes. We…
This paper shows how continuous data assimilation (CDA) can be used to provably enable and accelerate convergence of a (efficient at each iteration due to a physics-splitting, but generally slowly converging and not robust) nonlinear solver…
In this work, we introduce two algorithmic frameworks, named Bregman extragradient method and Bregman extrapolation method, for solving saddle point problems. The proposed frameworks not only include the well-known extragradient and…
After R.~Schoen completed the solution to the Yamabe problem, compact manifolds could be categorized into three classes, depending on whether they admit a metric with positive, non-negative, or only negative scalar curvature. Here we follow…
This paper develops a unified distributed method for solving two classes of constrained networked optimization problems, i.e., optimal consensus problem and resource allocation problem with non-identical set constraints. We first transform…
In this paper, we analyze gradient-free methods with one-point feedback for stochastic saddle point problems $\min_{x}\max_{y} \varphi(x, y)$. For non-smooth and smooth cases, we present analysis in a general geometric setup with arbitrary…
We present a novel accelerated primal-dual (APD) method for solving a class of deterministic and stochastic saddle point problems (SPP). The basic idea of this algorithm is to incorporate a multi-step acceleration scheme into the…
We consider non-convex optimization problems with constraint that is a product of simplices. A commonly used algorithm in solving this type of problem is the Multiplicative Weights Update (MWU), an algorithm that is widely used in game…