Mixed L2-Wasserstein optimal mapping between prescribed density functions

Journal of Optimization Theory and Applications

Volumn 111, Issue 2, 2001, Pages 255-271

  Benamou, J D ^a   Brenier, Y ^b  

^a INRIA   (France)

^b SORBONNE UNIVERSITÉ   (France)

Author keywords

Conjugate gradient algorithm; Least square distance; Monge Kantorovitch mass transfer problem; Optimal control; Wasserstein distance

Indexed keywords

CONJUGATE GRADIENT METHOD; COST FUNCTIONS; MAPPING; PROBLEM SOLVING;

CONJUGATE GRADIENT ALGORITHMS; COST-FUNCTION; FINAL DENSITY; LEAST SQUARES DISTANCES; MONGE-KANTOROVITCH MASS TRANSFER PROBLEM; OPTIMAL CONTROLS; OPTIMAL MAPPING; TIME DEPENDENT; TRANSFER PROBLEMS; WASSERSTEIN DISTANCE;

MASS TRANSFER;

EID: 0039002169     PISSN: 00223239     EISSN: None     Source Type: Journal    
DOI: 10.1023/a:1011926116573     Document Type: Article

References (7)

1. BENAMOU, J. D., and BRENIER, Y., A Computational Fluid Mechanics Solution to the Monge-Kantorovich Mass Transfer Problem, Numerische Mathematik, Vol. 84, pp. 375-393, 2000.
2. DOUGLAS, R. J., Decomposition of Weather Forecast Error Using Rearrangements of Functions, Preprint, 1998.
3. GLOWINSKI, R., Ensuring Well-Posedness by Analogy: Stokes Problem and Boundary Control for the Wave Equation, Journal of Computational Physics, Vol. 103, pp. 189-221, 1992.
4. GODLEWSKI, E., and RAVIART, P. A., Numerical Approximation of Hyperbolic Systems of Conservation Laws, Springer Verlag, New York, NY, 1996.
5. LIONS, J. L., Contrôle Optimal de Systèmes Gouvernés par des Equations aux Dérivées Partielles, Dunod, Paris, France, 1968.
6. SAAD, Y., and SCHULTZ, M. H., Conjugate Gradient-Like Algorithms for Solving Nonsymmetric Linear Systems, Mathematics of Computation, Vol. 44, pp. 417-424, 1985.
7. WHITAM, G. B., Linear and Nonlinear Waves, John Wiley and Sons, New York, NY, 1999.