Lectures on Optimal Transport
portes grátis
Lectures on Optimal Transport
Semola, Daniele; Ambrosio, Luigi; Brue, Elia
Springer International Publishing AG
01/2025
180
Mole
9783031768330
Pré-lançamento - envio 15 a 20 dias após a sua edição
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- 1. Lecture I. Preliminary notions and the Monge problem.- 2. Lecture II. The Kantorovich problem.- 3. Lecture III. The Kantorovich - Rubinstein duality.- 4. Lecture IV. Necessary and sufficient optimality conditions.- 5. Lecture V. Existence of optimal maps and applications.- 6. Lecture VI. A proof of the isoperimetric inequality and stability in Optimal Transport.- 7. Lecture VII. The Monge-Ampere equation and Optimal Transport on Riemannian manifolds.- 8. Lecture VIII. The metric side of Optimal Transport.- 9. Lecture IX. Analysis on metric spaces and the dynamic formulation of Optimal Transport.- 10. Lecture X.Wasserstein geodesics, nonbranching and curvature.- 11. Lecture XI. Gradient flows: an introduction.- 12. Lecture XII. Gradient flows: the Brezis-Komura theorem.- 13. Lecture XIII. Examples of gradient flows in PDEs.- 14. Lecture XIV. Gradient flows: the EDE and EDI formulations.- 15. Lecture XV. Semicontinuity and convexity of energies in the Wasserstein space.- 16. Lecture XVI. The Continuity Equation and the Hopf-Lax semigroup.- 17. Lecture XVII. The Benamou-Brenier formula.- 18. Lecture XVIII. An introduction to Otto's calculus.- 19. Lecture XIX. Heat flow, Optimal Transport and Ricci curvature.
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Optimal Transport;Gradient Flows;Partial Differential Equations;Analysis on Metric Spaces;Calculus of Variations
- 1. Lecture I. Preliminary notions and the Monge problem.- 2. Lecture II. The Kantorovich problem.- 3. Lecture III. The Kantorovich - Rubinstein duality.- 4. Lecture IV. Necessary and sufficient optimality conditions.- 5. Lecture V. Existence of optimal maps and applications.- 6. Lecture VI. A proof of the isoperimetric inequality and stability in Optimal Transport.- 7. Lecture VII. The Monge-Ampere equation and Optimal Transport on Riemannian manifolds.- 8. Lecture VIII. The metric side of Optimal Transport.- 9. Lecture IX. Analysis on metric spaces and the dynamic formulation of Optimal Transport.- 10. Lecture X.Wasserstein geodesics, nonbranching and curvature.- 11. Lecture XI. Gradient flows: an introduction.- 12. Lecture XII. Gradient flows: the Brezis-Komura theorem.- 13. Lecture XIII. Examples of gradient flows in PDEs.- 14. Lecture XIV. Gradient flows: the EDE and EDI formulations.- 15. Lecture XV. Semicontinuity and convexity of energies in the Wasserstein space.- 16. Lecture XVI. The Continuity Equation and the Hopf-Lax semigroup.- 17. Lecture XVII. The Benamou-Brenier formula.- 18. Lecture XVIII. An introduction to Otto's calculus.- 19. Lecture XIX. Heat flow, Optimal Transport and Ricci curvature.
Este título pertence ao(s) assunto(s) indicados(s). Para ver outros títulos clique no assunto desejado.
