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There exist excellent codes for an efficient numerical treatment of stiff and differential-algebraic problems. Let us mention {\sc Radau5} which is based on the $3$-stage Radau IIA collocation method, and its extension to problems with…

Numerical Analysis · Mathematics 2024-01-23 Nicola Guglielmi , Ernst Hairer

We introduce a fast and scalable method for solving quadratic programs with conditional value-at-risk (CVaR) constraints. While these problems can be formulated as standard quadratic programs, the number of variables and constraints grows…

Optimization and Control · Mathematics 2026-04-14 Eric Luxenberg , David Pérez-Piñeiro , Steven Diamond , Stephen Boyd

Deploying deep learning models on Internet of Things (IoT) devices often faces challenges due to limited memory resources and computing capabilities. Cooperative inference is an important method for addressing this issue, requiring the…

Distributed, Parallel, and Cluster Computing · Computer Science 2024-09-13 Zhibang Liu , Chaonong Xu , Zhizhuo Liu , Lekai Huang , Jiachen Wei , Chao Li

We propose a novel approach to solving input- and state-constrained parametric mixed-integer optimal control problems using Differentiable Predictive Control (DPC). Our approach follows the differentiable programming paradigm by learning an…

Systems and Control · Electrical Eng. & Systems 2025-06-25 Ján Boldocký , Shahriar Dadras Javan , Martin Gulan , Martin Mönnigmann , Ján Drgoňa

In this paper, we introduce a novel semi-analytical method for solving a broad class of initial value problems involving differential, integro-differential, and delay equations, including those with fractional and variable-order…

Numerical Analysis · Mathematics 2025-10-02 Mohamed Mostafa

This thesis focuses on developing and analyzing accelerated and inexact first-order methods for solving or finding stationary points of various nonconvex composite optimization (NCO) problems. The main tools mainly come from variational and…

Optimization and Control · Mathematics 2021-12-28 Weiwei Kong

In this paper, we introduce a higher-order multiscale method for time-dependent problems with highly oscillatory coefficients. Building on the localized orthogonal decomposition (LOD) framework, we construct enriched correction operators to…

Numerical Analysis · Mathematics 2026-05-15 Balaje Kalyanaraman , Felix Krumbiegel , Roland Maier , Siyang Wang

We introduce a family of implicit probabilistic integrators for initial value problems (IVPs), taking as a starting point the multistep Adams-Moulton method. The implicit construction allows for dynamic feedback from the forthcoming…

Methodology · Statistics 2019-04-19 Onur Teymur , Han Cheng Lie , Tim Sullivan , Ben Calderhead

This paper offers a matrix-free first-order numerical method to solve large-scale conic optimization problems. Solving systems of linear equations pose the most computationally challenging part in both first-order and second-order numerical…

Optimization and Control · Mathematics 2022-03-11 Muhammad Adil , Ramtin Madani , Sasan Tavakkol , Ali Davoudi

We present \texttt{DR-DAQP}, an open-source solver for strongly monotone affine variational inequaliries that combines Douglas-Rachford operator splitting with an active-set acceleration strategy. The key idea is to estimate the active set…

Systems and Control · Electrical Eng. & Systems 2026-04-06 Daniel Arnström , Emilio Benenati , Giuseppe Belgioioso

In this paper we propose a novel class of methods for high order accurate integration of multirate systems of ordinary differential equation initial-value problems. The proposed methods construct multirate schemes by approximating the…

Numerical Analysis · Mathematics 2022-12-23 Vu Thai Luan , Rujeko Chinomona , Daniel R. Reynolds

In this work, we provide a deep investigation of a family of arbitrary high order numerical methods for hyperbolic partial differential equations (PDEs), with particular emphasis on very high order versions, i.e., with order higher than 5.…

Numerical Analysis · Mathematics 2025-05-09 Lorenzo Micalizzi , Eleuterio F. Toro

Inverse problem or parameter estimation of ordinary differential equations (ODEs), the iterative process of minimizing the mismatch between model-predicted and experimental states by tuning the parameter values within an optimization…

Systems and Control · Electrical Eng. & Systems 2026-04-21 Siddharth Prabhu , Srinivas Rangarajan , Mayuresh Kothare

We introduce new planning and reinforcement learning algorithms for discounted MDPs that utilize an approximate model of the environment to accelerate the convergence of the value function. Inspired by the splitting approach in numerical…

Machine Learning · Computer Science 2022-11-28 Amin Rakhsha , Andrew Wang , Mohammad Ghavamzadeh , Amir-massoud Farahmand

To broaden the range of applicability of variable-order fractional differential models, reliable numerical approaches are needed to solve the model equation. In this paper, we develop Laguerre spectral collocation methods for solving…

Numerical Analysis · Mathematics 2018-04-05 M. A. Zaky , E. H. Doha , T. M. Taha , D. Baleanu

This study focuses on the numerical discretization methods for the continuous-time discounted linear-quadratic optimal control problem (LQ-OCP) with time delays. By assuming piecewise constant inputs, we formulate the discrete system…

Optimization and Control · Mathematics 2024-07-29 Zhanhao Zhang , Steen Hørsholt , John Bagterp Jørgensen

Fully implicit Runge-Kutta (IRK) methods have many desirable properties as time integration schemes in terms of accuracy and stability, but high-order IRK methods are not commonly used in practice with numerical PDEs due to the difficulty…

Numerical Analysis · Mathematics 2021-10-07 Ben S. Southworth , Oliver Krzysik , Will Pazner , Hans De Sterck

Integration of Ordinary Differential Equations (ODEs) using Backward Difference formula (BDF) methods with p backward steps achieves order p accuracy if specific conditions are met. This work extends the composition technique with complex…

Numerical Analysis · Mathematics 2026-05-11 Ahmad Deeb , Denys Dutykh , Maryam Al Zohbi

This paper introduces a unified framework for accelerated gradient methods through the variable and operator splitting (VOS). The operator splitting decouples the optimization process into simpler subproblems, and more importantly, the…

Optimization and Control · Mathematics 2025-05-08 Long Chen , Luo Hao , Jingrong Wei

We present two modified versions of the primal-dual splitting algorithm relying on forward-backward splitting proposed in \cite{vu} for solving monotone inclusion problems. Under strong monotonicity assumptions for some of the operators…

Optimization and Control · Mathematics 2013-03-13 Radu Ioan Bot , Ernö Robert Csetnek , Andre Heinrich