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Institution

Paris Dauphine University

EducationParis, France
About: Paris Dauphine University is a education organization based out in Paris, France. It is known for research contribution in the topics: Population & Approximation algorithm. The organization has 1766 authors who have published 6909 publications receiving 162747 citations. The organization is also known as: Paris Dauphine & Dauphine.


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TL;DR: This article introduces a new class of fast algorithms to approx-imate variational problems involving unbalanced optimal transport, and shows how these methods can be used to solve unbalanced transport, unbalanced gradient flows, and to compute unbalanced barycenters.
Abstract: This article introduces a new class of fast algorithms to approx-imate variational problems involving unbalanced optimal transport. While classical optimal transport considers only normalized probability distributions, it is important for many applications to be able to compute some sort of re-laxed transportation between arbitrary positive measures. A generic class of such “unbalanced” optimal transport problems has been recently proposed by several authors. In this paper, we show how to extend the, now classical, entropic regularization scheme to these unbalanced problems. This gives rise to fast, highly parallelizable algorithms that operate by performing only diagonal scaling (i.e. pointwise multiplications) of the transportation couplings. They are generalizations of the celebrated Sinkhorn algorithm. We show how these methods can be used to solve unbalanced transport, unbalanced gradient flows, and to compute unbalanced barycenters. We showcase applications to 2-D shape modification, color transfer, and growth models.

122 citations

Journal ArticleDOI
TL;DR: This paper proposes mathematical programs to infer veto-related parameters, first considering only one criterion, then all criteria simultaneously, using the original version of Electre outranking relation and two variants, and shows that these inference procedures lead tolinear programming, 0–1 linear programming, or separable programming problems, depending on the case.

122 citations

Journal ArticleDOI
TL;DR: In this article, the authors present a generalization of the Dirac-Fock model to the case of a spin-1/2 fermion, and present a new kind of Hardy-like inequalities and a stable algorithm to compute the eigenvalues.
Abstract: This review is devoted to the study of stationary solutions of lin- ear and nonlinear equations from relativistic quantum mechanics, involving the Dirac operator. The solutions are found as critical points of an energy func- tional. Contrary to the Laplacian appearing in the equations of nonrelativistic quantum mechanics, the Dirac operator has a negative continuous spectrum which is not bounded from below. This has two main consequences. First, the energy functional is strongly indefinite. Second, the Euler-Lagrange equations are linear or nonlinear eigenvalue problems with eigenvalues lying in a spectral gap (between the negative and positive continuous spectra). Moreover, since we work in the space domain R 3 , the Palais-Smale condition is not satisfied. For these reasons, the problems discussed in this review pose a challenge in the Calculus of Variations. The existence proofs involve sophisticated tools from nonlinear analysis and have required new variational methods which are now applied to other problems. In the first part, we consider the fixed eigenvalue problem for models of a free self-interacting relativistic particle. They allow to describe the localized state of a spin-1/2 particle (a fermion) which propagates without changing its shape. This includes the Soler models, and the Maxwell-Dirac or Klein- Gordon-Dirac equations. The second part is devoted to the presentation of min-max principles al- lowing to characterize and compute the eigenvalues of linear Dirac operators with an external potential, in the gap of their essential spectrum. Many con- sequences of these min-max characterizations are presented, among them a new kind of Hardy-like inequalities and a stable algorithm to compute the eigenvalues. In the third part we look for normalized solutions of nonlinear eigenvalue problems. The eigenvalues are Lagrange multipliers, lying in a spectral gap. We review the results that have been obtained on the Dirac-Fock model which is a nonlinear theory describing the behavior of N interacting electrons in an external electrostatic field. In particular we focus on the problematic definition of the ground state and its nonrelativistic limit. In the last part, we present a more involved relativistic model from Quan- tum Electrodynamics in which the behavior of the vacuum is taken into ac- count, it being coupled to the real particles. The main interesting feature of this model is that the energy functional is now bounded from below, providing us with a good definition of a ground state.

121 citations

Journal ArticleDOI
TL;DR: In this article, the authors systematically and rigorously investigate various stochastic volatility models used in Mathematical Finance and obtain necessary and sufficient conditions on the parameters, such as correlation, of these models in order to have integrable or L p solutions.
Abstract: We investigate here, systematically and rigorously, various stochastic volatility models used in Mathematical Finance. Mathematically, such models involve coupled stochastic differential equations with coefficients that do not obey the natural and classical conditions required to make these models “well-posed”. And we obtain necessary and sufficient conditions on the parameters, such as correlation, of these models in order to have integrable or L p solutions (for 1 p ∞ ).

120 citations


Authors

Showing all 1819 results

NameH-indexPapersCitations
Pierre-Louis Lions9828357043
Laurent D. Cohen9441742709
Chris Bowler8728835399
Christian P. Robert7553536864
Albert Cohen7136819874
Gabriel Peyré6530316403
Kerrie Mengersen6573720058
Nader Masmoudi6224510507
Roland Glowinski6139320599
Jean-Michel Morel5930229134
Nizar Touzi5722411018
Jérôme Lang5727711332
William L. Megginson5516918087
Alain Bensoussan5541722704
Yves Meyer5312814604
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Performance
Metrics
No. of papers from the Institution in previous years
YearPapers
202317
202291
2021371
2020408
2019415
2018392