MONGE-KANTOROVICH DUALITY THEORY AND ITS APPLICATION IN THE UTILITY THEORY
Table of contents
Share
QR
Metrics
MONGE-KANTOROVICH DUALITY THEORY AND ITS APPLICATION IN THE UTILITY THEORY
Annotation
PII
S042473880000616-6-1
Publication type
Article
Status
Published
Pages
143-165
Abstract
An article reviews the developments of duality theory for the Monge-Kantorovich general problem and its application in the utility theory.
Keywords
duality theory, Monge–Kantorovich duality, utility theory
Date of publication
02.10.2011
Number of purchasers
1
Views
838
Readers community rating
0.0 (0 votes)
Cite Download pdf
1

References



Additional sources and materials

1. Kantorovich L.V. (1942): O peremeshchenii mass // DAN. T. 37. № 7-8

2. Kantorovich L.V. (1948): Ob odnoj probleme Monzha // UMN. T. 3. № 2.

3. Kantorovich L.V., Akilov G.P. (1984): Funkcional'nyj analiz. M.: Nauka.

4. Kantorovich L.V., Rubinshtejn G.Sh. (1957): Ob odnom funkcional'nom prostranstve i nekotoryh ekstremal'nyh zadachah // DAN. T. 115.

5. Kantorovich L.V., Rubinshtejn G.Sh. (1958): Ob odnom prostranstve vpolne additivnyh funkcij // Vestnik LGU. Ser. mat., mekh. i astr. T. 13. № 7.

6. Kiruta A.Ya., Rubinov A.M., Yanovskaya E.B. (1980): Optimal'nyj vybor raspredelenij v slozhnyh social'no-ekonomicheskih zadachah. L.: Nauka.

7. Kuratovskij K. (1966): Topologiya. T. 1. M.: Mir.

8. Levin V.L. (1974): Dvojstvennost' i approksimaciya v zadache o peremeshchenii mass. V kn.: \"Matematicheskaya ekonomika i funkcional'nyj analiz\". M.: Nauka.

9. Levin V.L. (1975): K zadache o peremeshchenii mass // DAN. T. 224. № 5.

10. Levin V.L. (1977): O teoremah dvojstvennosti v zadache Monzha-Kantorovicha // UMN. T. 32. № 3.

11. Levin V.L. (1978): Zadacha Monzha-Kantorovicha o peremeshchenii mass. V kn.: \"Metody funkcional'nogo analiza v matematicheskoj ekonomike\". M.: Nauka.

12. Levin V.L. (1981): Nekotorye prilozheniya dvojstvennosti dlya zadachi o peremeshchenii mass s polunepreryvnoj snizu funkciej stoimosti. Zamknutye predpochteniya i teoriya Shoke // DAN. T. 260. № 2.

13. Levin V.L. (1983a): Teorema o nepreryvnoj poleznosti dlya zamknutyh predporyadkov na metrizuemomkompaktnom prostranstve // DAN. T. 273. № 4.

14. Levin V.L. (1983b): Teoremy ob izmerimoj poleznosti dlya zamknutyh i leksikograficheskih otnoshenij predpochteniya // DAN. T. 270. № 3.

15. Levin V.L. (1984): Zadacha o peremeshchenii mass v topologicheskom prostranstve i veroyatnostnye mery na proizvedenii dvuh prostranstv, obladayushchie zadannymi marginal'nymi merami // DAN. T. 276. № 5.

16. Levin V.L. (1984): Lipshicevy predporyadki i lipshicevy funkcii poleznosti // UMN. T. 39. № 6.

17. Levin V.L. (1985): Funkcional'no zamknutye predporyadki i sil'noe stohasticheskoe dominirovanie // DAN. T. 283. № 1.

18. Levin V.L. (1987): Izmerimye selektory mnogoznachnyh otobrazhenij i zadacha o peremeshchenii mass // DAN. T. 292. № 5.

19. Levin V.L. (1990): Formula dlya optimal'nogo znacheniya zadachi Monzha-Kantorovicha s gladkoj funkciej stoimosti i harakterizaciya ciklicheski monotonnyh otobrazhenij // Mat. sbornik. T. 181. № 12.

20. Levin V.L. (1996): Teoremy dvojstvennosti dlya netopologicheskogo varianta zadachi o peremeshchenii mass // DAN. T. 350. № 5.

21. Levin V.L. (1997): K teorii dvojstvennosti dlya netopologicheskih variantov zadachi o peremeshchenii mass // Mat. sbornik. T. 188. № 4.

22. Levin V.L. (1998): Sushchestvovanie i edinstvennost' sohranyayushchego meru optimal'nogo otobrazheniya v obshchej zadache Monzha-Kantorovicha // Funkcional'nyj analiz i ego prilozheniya. T. 32. № 3.

23. Levin V.L. (2002): Usloviya optimal'nosti dlya gladkih reshenij Monzha zadachi Monzha-Kantorovicha // Funkcional'nyj analiz i ego prilozheniya. T. 36. № 2.

24. Levin V.L. (2003): Reshenie zadach Monzha i Monzha-Kantorovicha: teoriya i primery // DAN. T. 388. № 1.

25. Levin V.L. (2004a): Metod v matematicheskoj teorii sprosa, svyazannyj s dvojstvennost'yu Monzha-Kantorovicha // DAN. T. 398. № 5.

26. Levin V.L. (2004b): Usloviya optimal'nosti i tochnye resheniya dvumernoj zadachi Monzha-Kantorovicha // Zapiski nauchnyh seminarov POMI. T. 312. Special'nyj vypusk \"Teoriya predstavlenij. Dinamicheskie sistemy XI\" (otv. red. A.M. Vershik).

27. Levin V.L. (2006): Zadachi nailuchshegopriblizheniya, svyazannye s dvojstvennost'yu Monzha-Kantorovicha // Mat. sbornik. T. 197. № 9.

28. Levin V.L. (2008a): O tipichnoj edinstvennosti optimal'nogo resheniya v beskonechnomernoj zadache linejnogo programmirovaniya // DAN. T. 421. № 1.

29. Levin V.L. (2008b): Gladkie dopustimye resheniya dvojstvennoj zadachi Monzha-Kantorovicha i ih primenenie v zadachah nailuchshego priblizheniya i matematicheskoj ekonomiki // DAN. T. 419. № 5.

30. Levin V.L. (2011): Obshchie predpochteniya i funkcii poleznosti. Podhod na osnove dvojstvennoj zadachi Kantorovicha // DAN. T. 437. № 5.

31. Levin V.L., Milyutin A.A. (1979): Zadacha o peremeshchenii mass s razryvnoj funkciej stoimosti i massovaya postanovka problemy dvojstvennosti vypuklyh ekstremal'nyh zadach // UMN. T. 34. № 3.

32. Marshall A.V., Olkin I. (1983): Neravenstva: Teoriya mazhorizacii i ee prilozheniya. M.: Mir.

33. Afriat S.N. (1967): The Construction of Utility Functions from Expenditure Data // Intern. Econ. Rev. Vol. 8.

34. Afriat S.N. (1973): On a System of Inequalities on Demand Analysis: an Extension of the Classical Method // Intern. Econ. Rev. Vol. 14.

35. Bridges D.S., Mehta G.B. (1995): Representations of Preference Orderings. LN in Economics and Mathem. Systems. Vol. 422. Springer.

36. Carlier G., Levin V.L., Shananin A.A. et al. (2002): A System of Inequalities Arising in Mathematical Economics and Connected with the Monge-Kantorovich Problem. Working Paper, Ceremade - UMR 7534 - Univ. Paris Dauphine.

37. d\'Aspremont C., Gevers L. (1977): Equity and the Informational Basis of Collective Choice // Rev. of Econ. Studies. Vol. 44.

38. Debreu G. (1954): Representation of a Preference Ordering by a Numerical Function. In: \"Decision Processes\". N.Y.: Wiley.

39. Debreu G. (1964): Continuity Properties of Paretian Utility // Intern. Econ. Rev. Vol. 5.

40. Houthakker H.S. (1950): Revealed Preference and the Utility Function // Economica. Vol. 17.

41. Kamae T., Krengel U., O\'Brien G.L. (1977): Stochastic Inequalities on Partially Ordered Spaces // Ann. Probab. Vol. 5.

42. Levin V.L. (1986): Extremal Problems with Probability Measures, Functionally Closed Preorders and Strong Stochastic Dominance. In: \"Stochastic Optimization\". LN in Control and Inform. Sci. Vol. 81. Springer. Berlin.

43. Levin V.L. (1990): General Monge-Kantorovich Problem and its Applications in Measure Theory and Mathematical Economics. In: \"Functional Analysis, Optimization, and Mathematical Economics (A collection of papers dedicated to memory of L.V. Kantorovich)\". L.J. Leifman (ed.) N.Y., Oxford: Oxford University Press.

44. Levin V.L. (1991): Some Applications of Set-Valued Mappings in Mathematical Economics // J. of Math. Econ. Vol. 20.

45. Levin V.L. (1996a): A Superlinear Multifunction Arising in Connection with Mass Transfer Problems // Set-Valued Analysis, Vol. 4.

46. Levin V.L. (1997a): Reduced Cost Functions and Their Applications // J. of Math. Econ. Vol. 28.

47. Levin V.L. (1997b): Topics in the Duality Theory for Mass Transfer Problem. In: \"Distributions with Given Marginals and Moment Problems\" BeneV., tĕpan J. (eds). Dordrecht: Kluwer.

48. Levin V.L. (1999): Abstract Cyclical Monotonicity and Monge Solutions for the General Monge-Kantorovich Problem // Set-Valued Analysis. Vol. 7.

49. Levin V.L. (2000): A Method in Utility Theory Connected with the Monge-Kantorovich Problem. Working Paper WP/2000/089. M.: CEMI.

50. Levin V.L. (2001a): On Generic Uniqueness of Optimal Solutions for the General Monge-Kantorovich Problem // Set-Valued Analysis. Vol. 9.

51. Levin V.L. (2001b): The Monge-Kantorovich Problems and Stochastic Preference Relations // Adv. Math. Econ. Vol. 3.

52. Levin V.L. (2004): Optimal Solutions of the Monge Problem // Adv. Math. Econ. Vol. 6.

53. Levin V.L. (2005): A Method in Demand Analysis Connected with the Monge-Kantorovich Problem // Adv. Math. Econ. Vol. 7.

54. Levin V.L. (2006): Abstract Convexity and the Monge-Kantorovich Duality. In: LN in Economics and Mathematical Systems. Vol. 583. Springer.

55. Levin V.L. (2008): On preference relations that admit smooth utility functions // Adv. Math. Econ. Vol. 11.

56. Levin V.L. (2009a): Smooth Feasible Solutions to a dual Monge-Kantorovich Problem with Applications to Best Approximation and Utility Theory in Mathematical Economics // Adv. Math. Econ. Vol. 12.

57. Levin V.L. (2009b): New Axiomatic Characterizations of Utilitarianism // Math. Soc. Sci. Vol. 58.

58. Levin V.L. (2010a): On Collective Utility Functions Admitting Linear Representations // J. of Math. Econ. Vol. 46.

59. Levin V.L. (2010b): On Social Welfare Functionals: Representation Theorems and Equivalence Classes // Math. Soc. Sci. Vol. 59.

60. Maskin E. (1978): A Theorem on Utilitarianism // Rev. of Econ. Studies. Vol. 45.

61. Preston C.J. (1974): A Generalization of the FKG Inequalities // Comm. Math. Phys. Vol. 36.

62. Sen A.K. (1970): Collective Choice and Social Welfare. San Francisco: Holden-Day.

63. Varian H.R. (1982): The Nonparametric Approach to Demand Analysis // Econometrica. Vol. 50.

64. Varian H.R. (1983): Non-Parametric Tests of Consumer Behaviour // The Rev. of Econ. Studies. Vol. V(1). № 160.

Comments

No posts found

Write a review
Translate