Vladimir L. Levin
Principal Researcher, Doctor of Sciences in MathematicsE-mail: vllevin (at) mail.ru
Selected Publications
(Links lead to full texts of papers in pdf format)
Monograph
Convex Analysis in Spaces of Measurable Functions and Its Application in Mathematics and Economics (in Russian). 1985. Nauka, Moscow, 352 p.
Selected Contributions to Books
Topics in the duality theory for mass transfer problems. - In: "Distributions with Given Marginals and Moment Problems" (V.Benes, J.Stepan, eds) 1997. Kluwer Academic Publishers, Dordrecht-Boston-London, pp.243-252.
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 the Memory of L.V.Kantorovich). (L.J.Leifman, ed.) 1990. Oxford University Press, N.Y. - Oxford, pp.141-176.
Convex analysis and extremal problems in functional spaces (in Russian). - A chapter in the collective monograph: "Mathematical Apparatus for Economics Modeling" (E.G.Golshtein, ed.) 1983. Nauka, Moscow, pp.164-189.
Theorems of convex analysis and guaranteed pro¯t under uncertainty (in Russian). - In: "Methods of the Theory of Extremal Problems in Economics" (V.L.Levin, ed.) 1981. Nauka, Moscow, pp.107-137.
The Monge-Kantorovich problem on mass transfer (in Russian). - In: "Methods of Functional Analysis in Mathematical Economics" (B.A.Efimov, ed.) 1978. Nauka, Moscow, pp.23-55.
Variational problems with functions of many variables and a model of resourses distribution (in Russian). - In: "Mathematical Economics and Functional Analysis" (B.S.Mityagin, ed.) 1974. Nauka, Moscow, pp.7-34 (with V.I.Arkin).
Duality and approximation in the problem of mass transfer (in Russian). - In: "Mathematical Economics and Functional Analysis" (B.S.Mityagin, ed.) 1974. Nauka, Moscow, pp.94-108.
Extremum conditions in infinite-dimensional linear problems with operator constraints (in Russian). - In: "Studies in Mathematical Programming" (E.G.Golshtein, ed.) 1968. Nauka, Moscow, pp.159-197.
Selected Articles
New axiomatic characterizations of utilitarianism. - Mathematical Social Sciences, v.58, 2009, pp. 15-24. [514 kB]
Smooth feasible solutions to a dual Monge - Kantorovich problem with applications to best approximation and utility theory in mathematical economics. - Advances in Mathematical Economics, v. 12, 2009, pp. 97-127. [569 kB]
On generic uniqueness of optimal solution in an infinite dimensional linear programming problem (in Russian). - Doklady Acad. Nauk 421, no.1, 2008, pp.21-23. English translation in: Doklady Mathematics, v. 78, no. 1, 2008, pp. 490-492. [206 kB]
Smooth feasible solutions to a dual Monge - Kantorovich problem and their application to the best approximation and mathematical economics problems (in Russian). - Doklady Acad. Nauk 419, no.5, 2008, pp.592-594. English translation in: Doklady Mathematics, v. 77, no. 2, 2008, pp. 281-283. [101 kB; 204 kB]
On preference relations that admit smooth utility functions. - Advances in Mathematical Economics, v.11, 2008, pp.95-104.
Abstract convexity and the Monge - Kantorovich duality. - In: "Generalized Convexity and Related Topics" (eds. I.V. Konnov, D.T. Luc, A.M. Rubinov), Lecture Notes in Economics and Mathematical Systems, vol. 583, Springer, Berlin - Heidelberg 2007, pp.33-72. [418 kB]
Two semiconic duality theorems. - Journal of Convex Analysis, v. 14, no. 4, 2007, pp.855-867.
Best approximation problems relating to Monge - Kantorovich duality (in Russian). - Matem. Sbornik 197, no.9, 2006, pp.103-114. English translation in: Sbornik: Mathematics 197, no. 9, 2006, pp.1353-1364. [278 kB]
A method in demand analysis connected with the Monge - Kantorovich problem. - Advances in Mathematical Economics, v. 7, 2005, pp. 47-93.
Optimality conditions and exact solutions to the two-dimensional Monge-Kantorovich problem (in Russian). - Notices of scientific seminars of the Steklov Mathematical Institute St-Petersburg Branch, vol.312, 2004, pp.150-164. English translation in: Journal of Mathematical Sciences 133, no.4, 2006, pp. 1456-1463.
Optimal solutions of the Monge problem. - Advances in Mathematical Economics, v. 6, 2004, pp. 85-122.
A method in mathematical demand theory connected with the Monge-Kantorovich duality (in Russian). - Doklady Acad. Nauk 398, no.5, 2004, pp.607-610. English translation in: Doklady Mathematics, v. 70, no. 2, 2004, pp. 770-773.
Abstract convexity in measure theory and in convex analysis. - Journal of Mathematical Sciences, v. 116, no. 4, 2003, pp. 3432-3467. [368 kB]
Functional analysis (in Russian). - In: "Economics and Mathematics Encyclopedic Dictionary" 2003, Great Russian Encyclopedia, Infra-M, Moscow, pp.570-571.
Infinite dimensional programming (in Russian). - In: "Economics and Mathematics Encyclopedic Dictionary" 2003, Great Russian Encyclopedia, Infra-M, Moscow, pp.32-33.
Solving the Monge and Monge - Kantorovich problems: theory and examples (in Russian). - Doklady Acad. Nauk 388, no.1, 2003, pp.7-10. English translation in: Doklady Mathematics 67, no. 1, 2003, pp. 1-4.
Optimality conditions for smooth Monge solutions of the Monge - Kantorovich problem (in Russian). - Functional Anal. Appl. 36, no.2, 2002, pp.38-44. English translation in: Funct. Anal. Appl. 36, no.2, 2002, pp. 114-119.
Alexei Alexeevich Milyutin (in Russian). - Uspekhi Matem. Nauk 57, no.3, 2002, pp.138-140 (with V.L.Bodneva, V.G.Boltianskii, I.M.Gelfand, V.V.Dikusar, A.V.Dmitruk, A.D.Ioffe, Ya.M.Kajdan, N.P.Osmolovskii, V.M.Tikhomirov, G.M.Henkin).
A model study of corruption under carrying out the privatization (in Russian). - Economics and Mathematical Methods 37, no.4, 2001, pp.85-102.
A model of privatization of indivisible goods under the conditions of corruption (in Russian). - Economics and Mathematical Methods 37, no.1, 2001, pp.77-90 (with M.I.Levin).
The Monge - Kantorovich problems and stochastic preference relations. - Advances in Mathematical Economics, v. 3, 2001, pp. 97-124.
On generic uniqueness of optimal solutions for the general Monge - Kantorovich problem. - Set-Valued Analysis, v. 9, 2001, pp. 383-390.
Semicinic duality in convex analysis (in Russian). - Trudy Moskovskogo Matem. Obcshestva 61, 2000, pp.210-253. English translation in: Trans. Moscow Math. Soc. 2000, pp. 197-238.
Dual representations of convex sets and Gateaux differentiability spaces. - Set-Valued Analysis, v. 7, 1999, pp. 133-157.
Abstract cyclical monotonicity and Monge solutions for the general Monge - Kantorovich problem. - Set-Valued Analysis, v. 7, 1999, pp. 7-32.
Equilibrium solutions of an auction game related to the model of privatization of indivisible boons under the conditions of corruption (in Russian). - Doklady Acad. Nauk 364, no.2, 1999, pp.178-180 (with M.I.Levin). English translation in: Doklady Mathematics 59, no.1, 1999, pp.154-156.
Existence and uniqueness of a measure-preserving optimal mapping in a general Monge - Kantorovich problem (in Russian). - Functional Anal. Appl. 32, no.3, 1998, pp.79-82. English translation in: Funct. Anal. And Its Applications, v. 32, no.3, 1998, pp. 205-208.
Equilibria and generalized equilibria in exchange models with indivisible commodities (in Russian). - Doklady Acad. Nauk 356, no.3, 1997, pp.299-302. English translation in: Doklady Mathematics 56, no.2, 1997, pp.696-699.
On duality theory for non-topological variants of the mass transfer problem (in Russian). - Matem. Sbornik 188, no.4, 1997, pp.95-126. English translation in: Sbornik: Mathematics 188, no.4, 1997, pp. 571-602.
Reduced cost functions and their applications. - Journal of Mathematical Economics, v.28, 1997, pp. 155-186.
Existence and uniqueness of a measure-preserving optimal mapping in a general Monge - Kantorovich problem (in Russian). - Functional Anal. Appl. 32, no.3, 1998, pp.79-82. English translation in: Doklady Mathematics 56, no.2, 1997, pp.696-699.
Semiconical sets, semihomogeneous functions, and a new scheme of duality in convex analysis (in Russian). - Doklady Acad. Nauk 354, no.5, 1997, pp.597-599. English translation in: Doklady Mathematics 55, no.3, 1997, pp. 421-423.
Duality for a non-topological version of the mass transportation problem. - In: "Distributions with Fixed Marginals and Related Topics" (eds. L. Rueschendorf, B. Schweizer and M.D. Taylor), Institute of Mathematical Statistics Lecture Notes - Monograph Series, vol. 28, 1996, Hayward, California, pp. 175-186. [569 kB]
A superlinear multifunction arising in connection with mass transfer problems. - Set-Valued Analysis, v. 4, 1996, pp. 41-65.
Duality theorems for a non-topological variant of the mass transfer problem (in Russian). - Doklady Acad. Nauk 350, no.5, 1996, pp.588-591. English translation in: Doklady Mathematics 54, no.2, 1996, pp. 741-744.
Dual representations of convex bodies and their polars (in Russian). - Functional Anal. Appl. 30, no.3, 1996, pp.79-81. English translation in: Funct. Anal. And Its Applications 30, 1996, pp. 209-210.
Quasi-convex functions and quasi-monotone operators. - Journal of Convex Analysis, v.2, 1995, pp. 167-172. [0.98 MB]
A characterization theorem for normal integrands with applications to descriptive function theory, functional analysis and nonconvex optimization. - Set-Valued Analysis, v. 2, 1994, pp. 395-414.
Exchange models with indivisible commodities, and implementation of competitive equilibria in games of auction type (in Russian). - Dokl. Akad. Nauk SSSR 334, no.1, 1994, pp.16-19. English translation in: Russian Acad. Sci. Dokl. Math. 49, no.1, 1994, pp. 15-19.
Measurable selectors of multivalued mappings with bianalytic graph and ¾igma-compact values (in Russian). - Trudy Moskovskogo Matem. Obcshestva 54, 1992, pp.3-28. English translation in: Trans. Moscow Math. Soc. 1993, pp. 1-22.
Some applications of set-valued mappings in mathematical economics. - Journal of Mathematical Economics, v. 20, 1991, pp. 69-87.
On a problem of convex analysis arising in optimal control theory (in Russian). - Matem. Zametki 47, no.5, 1990, pp.45-51.
A formula for the optimal value in the Monge-Kantorovich problem with a smooth cost function and a characterization of cyclically monotone mappings (in Russian). - Matem. Sbornik 181, no.12, 1990, pp.1694-1709. English translation in: Math. USSR -Sbornik 71, 1992, pp. 533-548.
New duality theorems for marginal problems with some applications in stochastics. - In: "Stability Problems for Stochastic Models". Lecture Notes in Math. 1412, 1989, pp.137-171 (with S.T.Rachev).
Solution of one problem of convex analysis (in Russian). - Uspekhi Mat. Nauk 42, no.2, 1987, pp.235-236.
Measurable selectors of multivalued mappings and mass transfer problem (in Russian). - Dokl. Akad. Nauk SSSR 292, no.5, 1987, pp.1048-1053. English translation in: Soviet Math. Doklady 35, no. 1, 1987, pp. 178-183.
Extremal problems with probability measures, functionally closed preorders and strong stochastic dominance. In: "Stochastic Optimization" (Proc. Internat. Conf. Kiev 1984, eds. V.I. Arkin, A. Shiraev, R. Wets). Lecture Notes in Control and Optimization Sciences 81, 1986, Springer, Berlin-Heidelberg-New York, pp.435-447.
Functionally closed preorders and strong stochastic dominance (in Russian). - Dokl. Akad. Nauk SSSR 283, no.1, 1985, pp.30-34. English translation in: Soviet Math. Doklady 32, no. 1, 1985, pp. 22-26.
Lipschitz preorders and Lipschitz utility functions (in Russian). - Uspekhi Mat. Nauk 39, no.6, 1984, pp.199-200.
The problem of mass transfer in a topological space and probability measures having given marginal measures on the product of two spaces (in Russian). - Dokl. Akad. Nauk SSSR 276, no.5, 1984, pp.1059-1064. English translation in: Soviet Math. Doklady 29, no. 3, 1984, pp. 638-643.
A continuous utility theorem for closed preorders on a ¾-compact metrizable space (in Russian). - Dokl. Akad. Nauk SSSR 273, no.4, 1983, pp.800-804. English translation in: Soviet Math. Doklady 28, ¹ 3, 1983, pp. 715-718.
Measurable utility theorems for closed and lexicographic preference relations (in Russian). - Dokl. Akad. Nauk SSSR 270, no.3, 1983, pp.542-546. English translation in: Soviet Math. Doklady 27, ¹ 3, 1983, pp. 639-643.
Some applications of the duality for the problem of translocation of masses with a lower semicontinuous cost function. Closed preferences and Choquet theory (in Russian). - Dokl. Akad. Nauk SSSR 260, no.2, 1981, pp.284-288. English translation in: Soviet Math. Doklady 24, 1981, pp. 262-267.
Measurable selections of multivalued mappings into topological spaces and upper envelopes of Caratheodory integrands (in Russian). - Dokl. Akad. Nauk SSSR 252, no.3, 1980, pp.535-539. English translation in: Soviet Math. Doklady 21, 1980, pp. 771-775.
The problem of mass transfer with a discontinuous cost function and a mass statement of the duality problem for convex extremal problems (in Russian). - Uspekhi Matem. Nauk 34, no.3, 1979, pp.3-68 (with A.A.Milyutin). English translation in: Russian Math. Surveys 34:3, 1979, pp.1-78.
On Borel sections of multivalued mappings (in Russian). - Sibirskii Matem. Journal 19, no.3, 1978, pp.617-623.
Measurable sections of multivalued mappings and projections of measurable sets (in Russian). - Functional Anal. Appl. 12, no.2, 1978, pp.40-45. English translation in: Functional Anal. Appl. 12:2, 1978, pp.108-112.
On duality theorems for the Monge-Kantorovich problem (in Russian). - Uspekhi Mat. Nauk 32, no.3, 1977, pp.171-172.
On subdifferentials and continuous extensions with preserving measurable dependence on parameter (in Russian). - Functional Anal. Appl. 10, no.3, 1976, pp.84-85.
Extremal problems with convex functionals that are lower semicontinuous relative to convergence in measure (in Russian). - Dokl. Akad. Nauk SSSR 224, no.6, 1975, pp.1256-1259. English translation in: Soviet Math. Dokl. 16, no.5, 1976, 1384-1388.
On the problem of mass transfer (in Russian). - Dokl. Acad. Nauk SSSR 224, no. 5, 1975, pp.1016-1019. English translation in: Soviet Math. Dokl. 16, 1975, pp.1349-1353.
Convex integral functionals and theory of lifting (in Russian). - Uspekhi Matem. Nauk 30, no. 2, 1975, pp.115-178. English translation in: Russian Math. Surveys 30:2, 1975, pp.119-184.
Lebesgue decomposition for functionals on the space of vector functions L1X (in Russian). - Functional Anal. Appl. 8, no.4, 1974, pp.48-53.
Subdifferentials of convex integral functionals and liftings identical on subspaces of L1 (in Russian). - Dokl. Akad. Nauk SSSR 211, no.5, 1973, pp.1046-1049. English translation in: Soviet Math. Dokl. 14, no. 4, 1973, pp. 1163-1166.
On the duality of some classes of linear operators acting between Banach spaces and Banach lattices (in Russian). - Sibirskii Matem. Journal 14, no.3, 1973, pp.599-608.
Subdifferentials of convex mappings and composite functions (in Russian). - Sibirskii Matem. Journal 13, no.6, 1972, pp.1295-1303.
Subdifferentials of convex functions (in Russian). - Trudy Moskovskogo Matem. Obcshestva 26, 1972, pp.3-73 (with A.D.Ioffe). English translation in: Trans. Moscow Math. Soc. (for the year 1972) 26, 1974, pp.1-72.
Convexity of values of vector integrals, measurable choice theorems and variational problems (in Russian). - Uspekhi Mat. Nauk 27, no.3, 1972, pp.21-77 (with V.I.Arkin). English translation in: Russian Mathematical Surveys 27:3, 1972, pp.21-85.
A variational problem with functions of several variables and operator constraints: maximum principle and existence theorem (in Russian). - Dokl. Akad. Nauk SSSR 200, no.1, 1971, pp.9-12. (with V.I.Arkin). English translation in: Soviet Math. Dokl. 12, no. 5, 1971, pp. 1293-1297.
Extreme points of some set of measurable vector functions of several variables and convexity of the values of vector integrals (in Russian). - Dokl. Akad. Nauk SSSR 199, no.6, 1971, pp.1223-1226. (with V.I.Arkin).
On the subdifferential of a composite functional (in Russian). - Dokl. Akad. Nauk SSSR 194, no.2, 1970, pp.268-269.
On subdifferentials of convex functionals (in Russian). - Uspekhi Mat. Nauk 25, no.4, 1970, pp.183-184.
On two classes of linear mappings acting between Banach spaces and Banach lattices (in Russian). - Sibirskii Matem. Journal 10, no.4, 1969, pp.903-909.
Applications of a theorem of E.Helly in convex programming, in the best approximation problems and in related topics (in Russian). - Matem. Sbornik 79, no.2, 1969, pp.250-263. English translation in: USSR Math. Sbornik 8, 1969, pp. 235-248.
Tensor products and functors determined by KB-lineals in categories of Banach spaces (in Russian). - Trudy Moskovskogo Matem. Obcshestva 20, 1969, pp.43-82. English translation in: Trans. Moscow Math. Soc. 20, 1969, pp.41-77.
On some properties of support functionals (in Russian). - Matem. Zametki 4, no.6, 1968, pp.685-696.
In¯nite dimensional analogues of a linear programming problem and a saddle point theorem (in Russian). - Uspekhi Mat. Nauk 23, no.3, 1968, pp.181-182.
Tensor products and functors determined by KB-lineals in categories of Banach spaces (in Russian). - Dokl. Akad. Nauk SSSR 163, no.5, 1965, pp.1058-1060.
Functors determined by KB-lineals in categories of Banach spaces (in Russian). - Dokl. Akad. Nauk SSSR 162, no.2, 1965, pp.262-265.
An open mapping theorem for uniform spaces (in Russian). - Mathematika. Izvestiya Vysshih Uchebnyh Zavedenii no.2(45), 1965, pp.86-90.
Closed graph theorems for uniform spaces (in Russian). - Dokl. Akad.Nauk SSSR 150, no.5, 1963, pp.981-983 (with D.A.Raikov).
Conditions for B-completeness of ultrabarreled and barreled spaces (in Russian). - Dokl. Akad. Nauk SSSR 145, no.2, 1962, pp.273-275.
On a class of locally convex spaces (in Russian). - Dokl. Akad. Nauk SSSR 145, no.1, 1962, pp.35-37.
On a theorem by A.I.Plesner (in Russian). - Uspekhi Mat. Nauk 16, no.5, 1961, pp.177-179.
On nondegenerate spectra of locally convex spaces (in Russian). - Dokl. Akad. Nauk SSSR 135, no.1, 1960, pp.12-15.