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Monotone Comparative Statics: Geometric Approach

Publications associées (32)

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Existence and Uniqueness of Maximal Regular Flows for Non-smooth Vector Fields

Maria Colombo

In this paper we provide a complete analogy between the Cauchy-Lipschitz and the DiPerna-Lions theories for ODE's, by developing a local version of the DiPerna-Lions theory. More precisely, we prove the existence and uniqueness of a maximal regular flow fo ...

2015

Variational Decomposition of Vector Fields in the Presence of Noise

Michaël Unser, Emrah Bostan, Pouya Dehghani Tafti

We present a variational framework, and an algorithm based on the alternating method of multipliers (ADMM), for the problem of decomposing a vector field into its curl- and divergence-free components (Helmholtz decomposition) in the presence of noise. We p ...

IEEE2013

Geodesic distance for right invariant Sobolev metrics of fractional order on the diffeomorphism group. II

Martins Bruveris, Martin Bauer

The geodesic distance vanishes on the group of compactly supported diffeomorphisms of a Riemannian manifold of bounded geometry, for the right invariant weak Riemannian metric which is induced by the Sobolev metric of order on the Lie algebra of vector fie ...

Springer Verlag2013

A Dual Algorithm for $ L _{ 1 } $ -Regularized Reconstruction of Vector Fields

Michaël Unser, Emrah Bostan, Pouya Dehghani Tafti

Recent advances in vector-field imaging have brought to the forefront the need for efficient denoising and reconstruction algorithms that take the physical properties of vector fields into account and can be applied to large volumes of data. With these req ...

IEEE2012

New Results in the Theory of Linear and Integer Programming

Nicolai Hähnle

The polynomial Hirsch conjecture states that the vertex-edge diameter of a d-dimensional polyhedron with n facets is bounded by a polynomial in d and n. For the special case where the polyhedron is defined as the set of points satisfying a system Ax ≤ b of ...

EPFL2012

A Dual Algorithm For L1-Regularized Reconstruction Of Vector Fields

Michaël Unser, Emrah Bostan, Pouya Dehghani Tafti

Ieee2012

Optimizing over the Growing Spectrahedron

Martin Jaggi

We devise a framework for computing an approximate solution path for an important class of parameterized semidefinite problems that is guaranteed to be ε-close to the exact solution path. The problem of computing the entire regularization path for matrix f ...

Springer Berlin Heidelberg2012

Approximation Algorithms for Modern Multi-Processor Scheduling Problems

Martin Niemeier

This thesis is devoted to the design and analysis of algorithms for scheduling problems. These problems are ubiquitous in the modern world. Examples include the optimization of local transportation, managing access to concurrent resources like runways at a ...

EPFL2012

Self-Similar Vector Fields

Pouya Dehghani Tafti

We propose statistically self-similar and rotation-invariant models for vector fields, study some of the more significant properties of these models, and suggest algorithms and methods for reconstructing vector fields from numerical observations, using the ...

EPFL2011

On Regularized Reconstruction of Vector Fields

Michaël Unser, Pouya Dehghani Tafti

In this paper, we give a general characterization of regularization functionals for vector field reconstruction, based on the requirement that the said functionals satisfy certain geometric invariance properties with respect to transformations of the coord ...

IEEE2011