English
Related papers

Related papers: Optimization based model order reduction for stoch…

200 papers

We introduce a class of numerical schemes for optimal control problems based on a novel Markov chain approximation, which uses, in turn, a piecewise constant policy approximation, Euler-Maruyama time stepping, and a Gauss-Hermite…

Optimization and Control · Mathematics 2020-01-07 Athena Picarelli , Christoph Reisinger

A finite horizon linear quadratic(LQ) optimal control problem is studied for a class of discrete-time linear fractional systems (LFSs) affected by multiplicative, independent random perturbations. Based on the dynamic programming technique,…

Optimization and Control · Mathematics 2016-07-01 J. J. Trujillo , V. M. Ungureanu

We consider the numerical solution of large-scale symmetric differential matrix Riccati equations. Under certain hypotheses on the data, reduced order methods have recently arisen as a promising class of solution strategies, by forming…

Numerical Analysis · Mathematics 2020-01-14 Gerhard Kirsten , Valeria Simoncini

We investigate the use of inexact solves for interpolatory model reduction and consider associated perturbation effects on the underlying model reduction problem. We give bounds on system perturbations induced by inexact solves and relate…

Numerical Analysis · Mathematics 2013-01-23 Christopher A. Beattie , Serkan Gugercin , Sarah Wyatt

This article describes a bridge between POD-based model order reduction techniques and the classical Newton/Krylov solvers. This bridge is used to derive an efficient algorithm to correct, "on-the-fly", the reduced order modelling of highly…

Classical Physics · Physics 2011-09-23 Pierre Kerfriden , Pierre Gosselet , Sondipon Adhikari , Stéphane Bordas

In this work we recast parametrized time dependent optimal control problems governed by partial differential equations in a saddle point formulation and we propose reduced order methods as an effective strategy to solve them. Indeed, on one…

Numerical Analysis · Mathematics 2023-08-08 Maria Strazzullo , Francesco Ballarin , Gianluigi Rozza

This contribution introduces a model order reduction approach for an advection-reaction problem with a parametrized reaction function. The underlying discretization uses an ultraweak formulation with an $L^2$-like trial space and an…

Numerical Analysis · Mathematics 2024-07-01 Christian Engwer , Mario Ohlberger , Lukas Renelt

Recent years have seen a growing interest in understanding acceleration methods through the lens of ordinary differential equations (ODEs). Despite the theoretical advancements, translating the rapid convergence observed in continuous-time…

Optimization and Control · Mathematics 2024-06-05 Zhonglin Xie , Wotao Yin , Zaiwen Wen

A widely used heuristic for solving stochastic optimization problems is to use a deterministic rolling horizon procedure, which has been modified to handle uncertainty (e.g. buffer stocks, schedule slack). This approach has been criticized…

Optimization and Control · Mathematics 2017-03-16 Raymond T. Perkins , Warren B. Powell

We propose a technique for reformulation of state and parameter estimation problems as that of matching explicitly computable definite integrals with known kernels to data. The technique applies for a class of systems of nonlinear ordinary…

Optimization and Control · Mathematics 2013-09-11 I. Yu. Tyukin , A. N. Gorban

We introduce a novel approach based on stochastic optimization to find the optimal sampling distribution for the data-driven stability analysis of switched linear systems. Our goal is to address limitations of existing approaches, in…

Optimization and Control · Mathematics 2025-09-01 Alexis Vuille , Guillaume O. Berger , Raphaël M. Jungers

In this contribution we propose reduced order methods to fast and reliably solve parametrized optimal control problems governed by time dependent nonlinear partial differential equations. Our goal is to provide a tool to deal with the time…

Numerical Analysis · Mathematics 2023-08-08 Francesco Ballarin , Gianluigi Rozza , Maria Strazzullo

Distributionally robust optimization (DRO) problems are increasingly seen as a viable method to train machine learning models for improved model generalization. These min-max formulations, however, are more difficult to solve. We therefore…

Machine Learning · Statistics 2020-11-03 Soumyadip Ghosh , Mark Squillante , Ebisa Wollega

We design receding horizon control strategies for stochastic discrete-time linear systems with additive (possibly) unbounded disturbances, while obeying hard bounds on the control inputs. We pose the problem of selecting an appropriate…

Optimization and Control · Mathematics 2011-07-07 Debasish Chatterjee , Peter Hokayem , John Lygeros

A high-ranking goal of interdisciplinary modeling approaches in the natural sciences are quantitative prediction of system dynamics and model based optimization. For this purpose, mathematical modeling, numerical simulation and scientific…

Optimization and Control · Mathematics 2015-03-17 Dominik Skanda , Dirk Lebiedz

Stochastic optimization problems often involve data distributions that change in reaction to the decision variables. This is the case for example when members of the population respond to a deployed classifier by manipulating their features…

Optimization and Control · Mathematics 2020-12-15 Dmitriy Drusvyatskiy , Lin Xiao

We consider optimal control problems for discrete-time random dynamical systems, finding unique perturbations that provoke maximal responses of statistical properties of the system. We treat systems whose transfer operator has an $L^2$…

Dynamical Systems · Mathematics 2022-09-21 Fadi Antown , Gary Froyland , Stefano Galatolo

In this work, we aim at efficiently solving a parametrized family of optimal transport problems by using model order reduction methods. We propose a reduced-order model by adding to the primal (respectively dual) version of the…

Numerical Analysis · Mathematics 2026-04-13 Elise Bonnet-Weill , Virginie Ehrlacher , Luca Nenna

In this work, we study the optimal discretization error of stochastic integrals, in the context of the hedging error in a multidimensional It\^{o} model when the discrete rebalancing dates are stopping times. We investigate the convergence,…

Probability · Mathematics 2014-05-19 Emmanuel Gobet , Nicolas Landon

In this contribution, a new framework for H2-optimal reduction of multiple-input, multiple- output linear dynamical systems by tangential interpolation is presented. The framework is motivated by the local nature of both tangential…

Numerical Analysis · Mathematics 2017-09-22 Alessandro Castagnotto , Boris Lohmann