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MATHICSE Technical Report : A Multilevel Stochastic Gradient method for PDE-constrained Optimal Control Problems with uncertain parameters

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An Adjoint Approach for Stabilizing the Parareal Method

Jan Sickmann Hesthaven, Allan Svejstrup Nielsen, Yvon Maday

The parareal algorithm seeks to extract parallelism in the time-integration direction of time-dependent differential equations. While it has been applied with success to a wide range of problems, it suffers from some stability issues when applied to non-di ...

2015

Designing Statistical Estimators That Balance Sample Size, Risk, and Computational Cost

Volkan Cevher

This paper proposes a tradeoff between computational time, sample complexity, and statistical accuracy that applies to statistical estimators based on convex optimization. When we have a large amount of data, we can exploit excess samples to decrease stati ...

Ieee-Inst Electrical Electronics Engineers Inc2015

This paper proposes a stability verification method for systems controlled by an early terminated first-order method (e.g., an MPC problem approximately solved by a fixed number of iterations of the fast gradient method). The method is based on the observa ...

Ieee2014

Stabilized multilevel Monte Carlo method for stiff stochastic differential equations

Adrian Blumenthal, Assyr Abdulle

A multilevel Monte Carlo (MLMC) method for mean square stable stochastic differential equations with multiple scales is proposed. For such problems, that we call stiff, the performance of MLMC methods based on classical explicit methods deteriorates becaus ...

Academic Press Inc Elsevier Science2013

Process Design and Optimization (MLS-S03): Model Identification by Gradient Methods

Julien Léo Billeter

This lecture describes the following topics: • Dynamic Models - Conservation of Mass (Concentration Measurements) - Conservation of Energy (Calorimetry) - Beer’s Law (Spectroscop ...

2013

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Kinetic models contribute greatly to cost reduction during the process development phase and are also helpful for process monitoring and control purposes. Kinetic models describe the underlying reactions, mass transport and operating conditions of the reac ...

2013

Computational Complexity Certification for Real-Time MPC With Input Constraints Based on the Fast Gradient Method

Colin Neil Jones

This paper proposes to use Nesterov's fast gradient method for the solution of linear quadratic model predictive control (MPC) problems with input constraints. The main focus is on the method's a priori computational complexity certification which consists ...

Institute of Electrical and Electronics Engineers2012

An analysis of a multiscale symmetric interior penalty discontinuous Galerkin finite element method for the numerical discretization of elliptic problems with multiple scales is proposed. This new method, first described in [A. Abdulle, C.R. Acad. Sci. Par ...

2012

Expected loss bounds for authentication in constrained channels

Serge Vaudenay, Christos Dimitrakakis, Aikaterini Mitrokotsa

We derive bounds on the expected loss for authenti-cation protocols in channels which are constrained due to noisyconditions and communication costs. This is motivated by anumber of authentication protocols, where at least some partof the authentication is ...

Ieee2012

Barycentric Bounds in Stochastic Programming: Theory and Application

Daniel Kuhn

The design and analysis of efficient approximation schemes are of fundamental importance in stochastic programming research. Bounding approximations are particularly popular for providing strict error bounds that can be made small by using partitioning tec ...

Springer New York2011