Smooth feasible solutions to a dual Monge–Kantorovich problem with applications to best approximation and utility theory in mathematical economics
作者： Vladimir L. Levin
DOI: 10.1007/978-4-431-92935-2_4
关键词: Dual (category theory) 、 Mathematics 、 Mathematical economics 、 Lebesgue integration 、 Lipschitz continuity 、 Interval (mathematics) 、 Utility theory 、 Preference (economics) 、 Class (set theory)
摘要: Given a (closed or open) subset X in R n , which is stable with respect to shifts positive directions, weconsider inequalities u(x) – u(y) ≤c(x,y),x,y ∈ X, and for wide class of functions c on × derive smooth solution these inequal ities from Lebesgue measurable one. Applications are given best approximation problem several problems mathematical economics relating preferences that admit (or Lipschitz continuous) utility functions, smooth-utility-rational choice, representations interval orders.
springer.com
rssi.ru 参考文章(33)
Vladimir L. Levin, A method in demand analysis connected with the Monge—Kantorovich problem Springer, Tokyo. pp. 47- 93 ,(2005) , 10.1007/4-431-27233-X_3
M Backmann, None, Lectu re Notes in Economics and Mathematical Systems ,(1975)
Vladimir L. Levin, Abstract Convexity and the Monge-Kantorovich Duality Springer, Berlin, Heidelberg. pp. 33- 72 ,(2007) , 10.1007/978-3-540-37007-9_2
Vladimir Levin, Abstract Cyclical Monotonicity and Monge Solutions for the General Monge–Kantorovich Problem Set-valued Analysis. ,vol. 7, pp. 7- 32 ,(1999) , 10.1023/A:1008753021652
V. L. Levin, Extremal problems with probability measures, functionally closed preorders and strong stochastic dominance Lecture Notes in Control and Information Sciences. pp. 435- 447 ,(1986) , 10.1007/BFB0007120
Mass transportation problems Springer. ,(1998) , 10.1007/B98893
Igor V Konnov, Alexander M Rubinov, None, Generalized convexity and related topics Lecture Notes in Economics and Mathematical Systems. ,(2006) , 10.1007/978-3-540-37007-9
H. H. McFaden, V. N Sudakov, Geometric Problems in the Theory of Infinite-dimensional Probability Distributions ,(1979)
Gerard Debreu, Gerard Debreu, Werner Hildenbrand, Mathematical Economics: Continuity properties of Paretian utility International Economic Review. ,vol. 5, pp. 163- 172 ,(1964) , 10.1017/CCOL052123736X.013
V L Levin, A A Milyutin, THE PROBLEM OF MASS TRANSFER WITH A DISCONTINUOUS COST FUNCTION AND A MASS STATEMENT OF THE DUALITY PROBLEM FOR CONVEX EXTREMAL PROBLEMS Russian Mathematical Surveys. ,vol. 34, pp. 1- 78 ,(1979) , 10.1070/RM1979V034N03ABEH003996