Concept

Symplectic manifold

Related publications (80)

Structure-Preserving Reduced Basis Methods for Hamiltonian Systems with a Nonlinear Poisson Structure

Jan Sickmann Hesthaven, Cecilia Pagliantini

We develop structure-preserving reduced basis methods for a large class of problems by resorting to their semi-discrete formulation as Hamiltonian dynamical systems. In this perspective, the phase space is naturally endowed with a Poisson manifold structur ...

2018

Structure-Preserving Reduced Basis Methods for Hamiltonian Systems with a State-dependent Poisson Structure

Jan Sickmann Hesthaven, Cecilia Pagliantini

We develop structure-preserving reduced basis methods for a large class of nondissipative problems by resorting to their formulation as Hamiltonian dynamical systems. With this perspective, the phase space is naturally endowed with a Poisson manifold struc ...

2018

A Lagrangian relaxation technique for the demand-based benefit maximization problem

Michel Bierlaire, Shadi Sharif Azadeh, Virginie Janine Camille Lurkin, Meritxell Pacheco Paneque, Bernard Gendron

The integration of discrete choice models with Mixed Integer Linear Programming (MILP) models provides a better understanding of customers' preferences to operators while planning for their systems. However, the formulations associated with the former are ...

2018

A Lagrangian relaxation technique for the demand-based benefit maximization problem

Michel Bierlaire, Shadi Sharif Azadeh, Virginie Janine Camille Lurkin, Meritxell Pacheco Paneque, Bernard Gendron

The integration of discrete choice models in Mixed Integer Linear Programming (MILP) models provides a better understanding of the preferences of the customers to the operators while planning for their systems. However, the formulations associated with ch ...

2018

A Lagrangian relaxation technique for the demand-based benefit maximization problem

Michel Bierlaire, Shadi Sharif Azadeh, Virginie Janine Camille Lurkin, Meritxell Pacheco Paneque, Bernard Gendron

Discrete choice models are the state-of-the-art of demand modeling at the disaggregate level. Their integration with Mixed Integer Linear Programming (MILP) models provides a better understanding of customers' preferences to operators while planning for t ...

2018

Structure-Preserving Model-Reduction of Dissipative Hamiltonian Systems

Jan Sickmann Hesthaven, Babak Maboudi Afkham

Reduced basis methods are popular for approximately solving large and complex systems of dierential equations. However, conventional reduced basis methods do not generally preserve conservation laws and symmetries of the full order model. Here, we present ...

2017

The tropical momentum map: a classification of toric log symplectic manifolds

Tudor Ratiu

We give a generalization of toric symplectic geometry to Poisson manifolds which are symplectic away from a collection of hypersurfaces forming a normal crossing configuration. We introduce the tropical momentum map, which takes values in a generalization ...

Springer Verlag2017

Motivic and p-adic Localization Phenomena

Dimitri Stelio Wyss

In this thesis we compute motivic classes of hypertoric varieties, Nakajima quiver varieties and open de Rham spaces in a certain localization of the Grothendieck ring of varieties. Furthermore we study the

p

-adic pushforward of the Haar measure under a ...

EPFL2017

Structure preserving model reduction of parametric Hamiltonian systems

Jan Sickmann Hesthaven, Babak Maboudi Afkham

While reduced-order models (ROMs) are popular for approximately solving large systems of differential equations, the stability of reduced models over long-time integration remains an open question. We present a greedy approach for ROM generation of paramet ...

2017

On the Lagrangian structure of transport equations: The Vlasov–Poisson system

Maria Colombo

The Vlasov-Poisson system is an important nonlinear transport equation, used to describe the evolution of particles under their self-consistent electric or gravitational field. The existence of classical solutions is limited to dimensions d

2017

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Motivic and p-adic Localization Phenomena

Dimitri Stelio Wyss

p

-adic pushforward of the Haar measure under a ...

EPFL2017