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We introduce a new class of arbitrary-order exponential time differencing methods based on spectral deferred correction (ETDSDC) and describe a simple procedure for initializing the requisite matrix functions. We compare the stability and…

Numerical Analysis · Mathematics 2020-11-03 Tommaso Buvoli

Practical implementations of active disturbance rejection control (ADRC) will almost always take place in discretized form. Since applications may have quite different needs regarding their discrete-time controllers, this article summarizes…

Systems and Control · Electrical Eng. & Systems 2023-04-27 Gernot Herbst , Rafal Madonski

In this paper, we propose an adaptive step size strategy for a class of line search methods for orthogonality constrained minimization problems, which avoids the classic backtracking procedure. We prove the convergence of the line search…

Optimization and Control · Mathematics 2020-02-21 Xiaoying Dai , Liwei Zhang , Aihui Zhou

An alternative first step approximation based on subgrid artificial viscosity modeling (SAV) is proposed for defect-deferred correction method (DDC) for incompresible Navier-Stokes equation at high Reynolds number. This new approach not…

Numerical Analysis · Mathematics 2020-06-02 Mustafa Aggul

In this paper, we demonstrate that the explicit ADER approach as it is used inter alia in [1] can be seen as a special interpretation of the deferred correction (DeC) method as introduced in [2]. By using this fact, we are able to embed…

Numerical Analysis · Mathematics 2022-11-17 Maria Han Veiga , Philipp Öffner , Davide Torlo

The spectral deferred correction (SDC) method is an iterative scheme for computing a higher-order collocation solution to an ODE by performing a series of correction sweeps using a low-order timestepping method. This paper examines a…

Numerical Analysis · Mathematics 2015-10-09 Robert Speck , Daniel Ruprecht , Matthew Emmett , Michael Minion , Matthias Bolten , Rolf Krause

We consider the dynamics of a parabolic and a hyperbolic equation coupled on a common interface and develop time-stepping schemes that can use different time-step sizes for each of the subproblems. The problem is formulated in a strongly…

Numerical Analysis · Mathematics 2020-07-13 Martyna Soszynska , Thomas Richter

The response to a setpoint change in PID controlled feedback systems plays an important role for the tuning methods. This response may be easily evaluated in linear systems without delay by solving the related ordinary differential…

Optimization and Control · Mathematics 2007-05-23 Gianpasquale Martelli

Tuning the step size of stochastic gradient descent is tedious and error prone. This has motivated the development of methods that automatically adapt the step size using readily available information. In this paper, we consider the family…

Machine Learning · Computer Science 2024-11-13 Robert M. Gower , Mathieu Blondel , Nidham Gazagnadou , Fabian Pedregosa

The Primal-Dual hybrid gradient (PDHG) method is a powerful optimization scheme that breaks complex problems into simple sub-steps. Unfortunately, PDHG methods require the user to choose stepsize parameters, and the speed of convergence is…

Numerical Analysis · Mathematics 2015-03-25 Tom Goldstein , Min Li , Xiaoming Yuan , Ernie Esser , Richard Baraniuk

In scalable machine learning systems, model training is often parallelized over multiple nodes that run without tight synchronization. Most analysis results for the related asynchronous algorithms use an upper bound on the information…

Machine Learning · Computer Science 2022-04-12 Xuyang Wu , Sindri Magnusson , Hamid Reza Feyzmahdavian , Mikael Johansson

Adaptive designs have been proposed for clinical trials in which the nuisance parameters or alternative of interest are unknown or likely to be misspecified before the trial. Whereas most previous works on adaptive designs and mid-course…

Methodology · Statistics 2011-05-18 Jay Bartroff , Tze Leung Lai

In this work, we propose new adaptive step size strategies that improve several stochastic gradient methods. Our first method (StoPS) is based on the classical Polyak step size (Polyak, 1987) and is an extension of the recent development of…

Machine Learning · Computer Science 2022-08-11 Samuel Horváth , Konstantin Mishchenko , Peter Richtárik

Adaptive atomistic/continuum (a/c) coupling method is an important method for the simulation of material and atomistic systems with defects to achieve the balance of accuracy and efficiency. Residual based a posteriori error estimator is…

Numerical Analysis · Mathematics 2022-11-28 Yangshuai Wang , Hao Wang

We construct a high-order adaptive time stepping scheme for vesicle suspensions with viscosity contrast. The high-order accuracy is achieved using a spectral deferred correction (SDC) method, and adaptivity is achieved by estimating the…

Numerical Analysis · Mathematics 2014-09-02 Bryan Quaife , George Biros

With the increasing number of compute components, failures in future exa-scale computer systems are expected to become more frequent. This motivates the study of novel resilience techniques. Here, we extend a recently proposed…

Mathematical Software · Computer Science 2018-04-18 Markus Huber , Ulrich Rüde , Barbara Wohlmuth

We present adaptive gradient methods (both basic and accelerated) for solving convex composite optimization problems in which the main part is approximately smooth (a.k.a. $(\delta, L)$-smooth) and can be accessed only via a (potentially…

Optimization and Control · Mathematics 2024-06-11 Anton Rodomanov , Xiaowen Jiang , Sebastian Stich

This paper introduces a generalization of the well-known Riccati recursion for solving the discrete-time equality-constrained linear quadratic optimal control problem. The recursion can be used to compute the solutions as well as optimal…

Optimization and Control · Mathematics 2024-12-31 Lander Vanroye , Joris De Schutter , Wilm Decré

Adaptive gradient methods have shown their ability to adjust the stepsizes on the fly in a parameter-agnostic manner, and empirically achieve faster convergence for solving minimization problems. When it comes to nonconvex minimax…

Optimization and Control · Mathematics 2025-10-10 Xiang Li , Junchi Yang , Niao He

We suggest a simple adaptive step-size procedure, which does not require any line-search, for a general class of nonlinear optimization methods and prove convergence of a general method under mild assumptions. In particular, the goal…

Optimization and Control · Mathematics 2018-03-05 Igor Konnov