4.3 Article

EXISTENCE AND UNIQUENESS OF OPTIMAL TRANSPORT MAPS OBTAINED BY THE SECONDARY VARIATIONAL METHOD

Related references

Note: Only part of the references are listed.
Article Automation & Control Systems

The multimarginal optimal transport formulation of adversarial multiclass classification

Nicolas Garcia Trillos et al.

Summary: This study examines a family of adversarial multiclass classification problems and provides equivalent reformulations using two different approaches. The results reveal the geometric structure of these problems and extend previous findings in binary classification. Furthermore, computational implications suggest that our solutions can recover optimal classification rules and adversarial strategies for the original problem.

JOURNAL OF MACHINE LEARNING RESEARCH (2023)

Article Mathematics, Applied

IMAGE SEGMENTATION VIA L1 MONGE-KANTOROVICH PROBLEM

Yupeng Li et al.

INVERSE PROBLEMS AND IMAGING (2019)

Article Mathematics

On Sudakov's Type Decomposition of Transference Plans with Norm Costs

Stefano Bianchini et al.

MEMOIRS OF THE AMERICAN MATHEMATICAL SOCIETY (2018)

Article Mathematics, Applied

Optimal transportation in for a distance cost with a convex constraint

Ping Chen et al.

ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK (2015)

Article Mathematics, Applied

Optimal transportation for a quadratic cost with convex constraints and applications

C. Jimenez et al.

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES (2012)

Article Mathematics

THE MONGE PROBLEM IN Rd

Thierry Champion et al.

DUKE MATHEMATICAL JOURNAL (2011)

Article Mathematics

A proof of Sudakov theorem with strictly convex norms

Laura Caravenna

MATHEMATISCHE ZEITSCHRIFT (2011)

Article Mathematics, Applied

The Monge problem for strictly convex norms in R-d

Thierry Champion et al.

JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY (2010)

Article Mathematics, Applied

Absolute continuity and summability of transport densities: simpler proofs and new estimates

Filippo Santambrogio

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS (2009)

Article Mathematics, Applied

The infinity-Wasserstein distance: Local solutions and existence of optimal transport maps

Thierry Champion et al.

SIAM JOURNAL ON MATHEMATICAL ANALYSIS (2008)

Article Mathematics

Existence of optimal transport maps for crystalline norms

L Ambrosio et al.

DUKE MATHEMATICAL JOURNAL (2004)

Article Mathematics, Applied

Uniqueness and transport density in Monge's mass transportation problem

M Feldman et al.

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS (2002)

Article Mathematics, Applied

On the Monge mass transfer problem

NS Trudinger et al.

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS (2001)