Кутателадзе С. С.
Владикавказский математический журнал. 2015. Том 17. Выпуск 3.С.93-100.
Аннотация: Краткое обсуждение некоторых разделов выпуклой геометрии, функционального анализа, оптимизации и нестандартных моделей в сфере интересов автора.
Ключевые слова: выпуклые задачи изопериметрического типа, Парето-оптимальность, \(\varepsilon\)-программирование, булевозначный анализ, инфинитезимальный анализ.
1. Bacon F. The Tvvoo Bookes of Francis Bacon, of the Proficience and Aduancement of Learning, Diuine and Humane. To the King.---London: Printed for Henrie Tomes, 1605.---URL: http://ebooks.adelaide.edu.au/b/bacon/francis/b12a/complete.html
2. Euler L. Specimen de Usu Observationum in Mathesi Pura // Novi Commentarii Academiae Scientiarum Petropolitanae.---1761.---Vol. 6.---P. 185--230.---URL: http://eulerarchive.maa.org/pages/E256.html.
3. Feferman S. In Light of Logic.---N.Y. and Oxford: Oxford University Press, 1998.
4. Reshetnyak Yu. G. On the Length and Swerve of a Curve and the Area of a Surface (PhD Thesis).---Leningrad: Leningrad State University, 1954.---[in Russian].
5. Alexandrov A. D. Selected Works. Vol. 1: Geometry and Applications.---Novosibirsk: Nauka, 2006.---[in Russian].
6. Kutateladze S. S. and Rubinov A. M. Minkowski Duality and Its Applications // Russian Math. Surveys.---1972.---Vol. 27, № 3.---P. 137--191.
7. Singer I. Abstract Convex Analysis.---N.Y.: John Wiley, 1997.
8. Urysohn P. S. Dependence Between the Average Width and Volume of Convex Bodies // Mat. Sb.--1924.---Vol. 31, № 3.---P. 477--486.---[in Russian].
9. Pogorelov A. V. Imbedding a `Soap Bubble' into a Tetrahedron // Math. Notes.---1994.---Vol. 56, № 2.---P. 824--826.
10. Kantorovich L. V. On Semiordered Linear Spaces and Their Applications in the Theory of Linear Operators // Dokl. Akad. Nauk SSSR.---1935.---Vol. 4, № 1--2.---P. 11--14.---[in Russian].
11. Chernikov S. N. Linear Inequalities.---Moscow: Nauka, 1968.---[in Russian].
12. Kutateladze S. S. Modules Admitting Convex Analysis // Soviet Math. Dokl.---1980.---Vol. 21, № 3.---P. 820--823.
14. Kutateladze S. S. Choquet Boundaries in \(K\)-Spaces // Russian Math. Surveys.---1975.---Vol. 30, № 4.---P. 115--155.
15. Kolokol'tsov V. N. and Maslov V. P. Idempotent Analysis as a Tool of Control Theory and Optimal Synthesis. I // Funct. Anal. Appl.---1989.---Vol. 23, № 1.---P. 1--11.
16. Kutateladze S. S. Convex Operators // Russian Math. Surveys.---1979.---Vol. 34, № 1.---P. 181--214.
17. Rubinov A. M. Sublinear Operators and Their Applications // Russian Math. Surveys.---1977.---Vol. 32, № 4.---P. 115--175.
18. Tikhomirov V. M. Convex Analysis // Current Problems in Mathematics. Fundamental Trends.---Moscow: VINITI, 1987.---Vol. 14.---P. 5--101.---[in Russian].
19. Gutierrez C., Jimenez B., and Novo V. On Approximate Solutions in Vector Optimization Problems via Scalarization // Computat. Optim. Appl.---2006.---Vol. 35.---P. 305--324.
20. Kutateladze S. S. Multiobjective Problems of Convex Geometry // Sib. Math. J.---2009.---Vol. 50, № 5.---P. 887--897.
21. Kutateladze S. S. Multiple Criteria Problems over Minkowski Balls // J. Appl. Indust. Math.---2013.---Vol. 7, № 2.---P. 208--214.
22. Kutateladze S. S. A Variant of Nonstandard Convex Programming // Sib. Math. J.---1986.---Vol. 27, № 4.---P. 537--544.
23. Scott D. Boolean Models and Nonstandard Analysis // Applications of Model Theory to Algebra, Analysis, and Probability.---New York: Holt, Rinehart and Winston, 1969.---P. 87--92.
24. Takeuti G. Two Applications of Logic to Mathematics.---Tokyo and Princeton: Iwanami Publ. & Princeton Univ. Press, 1978.
25. Kusraev A. G. and Kutateladze S. S. Introduction to Booolean Valued Analysis.---Moscow: Nauka, 2005.---[in Russian].
26. Gordon E. I., Kusraev A. G., and Kutateladze S. S. Infinitesimal Analysis: Selected Topics.---Moscow: Nauka, 2011.---[in Russian].
27. Kusraev A. G. and Kutateladze S. S. Boolean Valued Analysis: Selected Topics.---Vladikavkaz: Southern Math. Institute, 2014.
28. Gordon E. I. Real numbers in Boolean-valued models of set theory and \(K\)-spaces // Dokl. Akad. Nauk SSSR.---1977.---Vol. 237, № 4, P. 773--775.
29. Kutateladze S. S. On Grothendieck Subspaces // Sib. Math. J.---2005.---Vol. 46, № 3.---P. 489--493.
30. Kutateladze S. S. The Farkas Lemma Revisited // Sib. Math. J.---2010.---Vol. 51, № 1.---P. 78--87.
31. Kutateladze S. S. The Polyhedral Lagrange Principle // Sib. Math. J.---2011.---Vol. 52, № 3.---P. 484--486.
