01.01.09 (Discrete mathematics and mathematical cybernetics)
Birth date:
6.08.1949
E-mail:
Keywords:
nonsmooth analysis; nondifferentiable optimization; maximin; differential properties of marginal functions; distance function; estimation of a complex sets by a simplest sets.
Graduated from Faculty of Mathematics and Mechanics of Saratov State University (SGU) in 1971 (department of mathematical analysis). Ph.D. thesis was defended in 1987. D.Sci. thesis was defended in 1997. A list of my works contains more than 40 titles. Since 1997 I and A. P. Khromov have led the research seminar at SGU on nonsmooth analysis and extremal problems.
Main publications:
Dudov S. I. Differentsiruemost po napravleniyam funktsii rasstoyaniya // Matem. sbornik, 1995, 186(3), 29–52.
Dudov S. I. Vnutrennyaya otsenka vypuklogo mnozhestva telom normy // Zhurnal vychisl. matem. i matem. fiziki, 1996, 36(5), 153–159.
Dudov S. I. Subdifferentsiruemost i superdifferentsiruemost funktsii rastoyaniya. Matem. zametki, 1997, 61(4), 530–542.
Dudov S. I. Vypuklye i vognutye approksimatsii funktsii rasstoyaniya // Kibernetika i sistemnyi analiz, 1998, 3, 104–116.
Dudov S. I., Zlatorunskaya I. V. Ravnomernaya otsenka vypuklogo kompakta sharom proizvolnoi normy // Matem. sbornik, 2000, 191(10), 13–38.
S. I. Dudov, M. A. Osiptsev, “On one consequence of the Chebyshev alternance”, Izv. Saratov Univ. Math. Mech. Inform., 25:1 (2025), 4–14
2022
2.
S. I. Dudov, M. A. Osiptsev, “Sufficient Conditions for a Minimum of a Strongly Quasiconvex Function on a Weakly Convex Set”, Mat. Zametki, 111:1 (2022), 39–53; Math. Notes, 111:1 (2022), 33–46
S. I. Dudov, M. A. Osiptsev, “Distance between strongly and weakly convex sets”, Izv. Saratov Univ. Math. Mech. Inform., 21:4 (2021), 434–441
4.
S. I. Dudov, M. A. Osiptsev, “Characterization of solutions of strong-weak convex programming problems”, Mat. Sb., 212:6 (2021), 43–72; Sb. Math., 212:6 (2021), 782–809
V. V. Abramova, S. I. Dudov, M. A. Osiptsev, “The external estimate of the compact set by Lebesgue set of the convex function”, Izv. Saratov Univ. Math. Mech. Inform., 20:2 (2020), 142–153
S. I. Dudov, E. S. Polovinkin, V. V. Abramova, “Properties of the distance function to strongly and weakly convex sets in a nonsymmetrical space”, Izv. Vyssh. Uchebn. Zaved. Mat., 2020, no. 5, 22–38; Russian Math. (Iz. VUZ), 64:5 (2020), 17–30
S. I. Dudov, M. A. Osiptsev, “A Formula for the Superdifferential of the Distance Determined by the Gauge Function to the Complement of a Convex Set”, Mat. Zametki, 106:5 (2019), 660–668; Math. Notes, 106:5 (2019), 703–710
8.
V. V. Abramova, S. I. Dudov, A. V. Zharkova, “The formula for the subdifferential of the distance function to a convex set in an nonsymmetrical space”, Vestnik S.-Petersburg Univ. Ser. 10. Prikl. Mat. Inform. Prots. Upr., 15:3 (2019), 300–309
9.
S. I. Dudov, M. A. Osiptsev, “Spherical shell of the boundary of a compact set with a minimum cross-sectional area formed by a two-dimensional plane”, Zh. Vychisl. Mat. Mat. Fiz., 59:1 (2019), 169–182; Comput. Math. Math. Phys., 59:1 (2019), 160–173
2017
10.
S. I. Dudov, V. V. Abramova, “On an inner estimate of a convex body by the Lebesgue set of convex differentiable function”, Izv. Saratov Univ. Math. Mech. Inform., 17:3 (2017), 267–275
2016
11.
S. I. Dudov, M. A. Osiptsev, “Stability of best approximation of a convex body by a ball of fixed radius”, Zh. Vychisl. Mat. Mat. Fiz., 56:4 (2016), 535–550; Comput. Math. Math. Phys., 56:4 (2016), 525–540
S. I. Dudov, M. A. Osiptsev, “On functional stability of the solution for the problem of convex body best approximating by a ball with fixed radius”, Izv. Saratov Univ. Math. Mech. Inform., 15:3 (2015), 273–279
13.
S. I. Dudov, E. A. Meshcheryakova, “On asphericity of convex body”, Izv. Vyssh. Uchebn. Zaved. Mat., 2015, no. 2, 45–58; Russian Math. (Iz. VUZ), 59:2 (2015), 36–47
S. I. Dudov, M. A. Osipcev, “On an Approach to Approximate Solving of the Problem for the Best Approximation for Compact Body by a Ball of Fixed Radius”, Izv. Saratov Univ. Math. Mech. Inform., 14:3 (2014), 267–272
S. I. Dudov, E. A. Meshcheryakova, “Method for finding an approximate solution of the asphericity problem for a convex body”, Zh. Vychisl. Mat. Mat. Fiz., 53:10 (2013), 1668–1678; Comput. Math. Math. Phys., 53:10 (2013), 1483–1493
S. I. Dudov, E. V. Sorina, “Uniform estimate for a segment function in terms of a polynomial strip”, Algebra i Analiz, 24:5 (2012), 44–71; St. Petersburg Math. J., 24:5 (2013), 723–742
S. I. Dudov, E. A. Mesheryakova, “The characteristic of stability of the solution in the problem of convex compact set asphericity”, Izv. Saratov Univ. Math. Mech. Inform., 11:2 (2011), 20–26
S. I. Dudov, E. V. Sorina, “Uniform estimation of a segment function by a polynomial strip of fixed width”, Zh. Vychisl. Mat. Mat. Fiz., 51:11 (2011), 1981–1994; Comput. Math. Math. Phys., 51:11 (2011), 1864–1877
S. I. Dudov, E. A. Mesheryakova, “On a approximate solution of the problem of aspherical convex compact set”, Izv. Saratov Univ. Math. Mech. Inform., 10:4 (2010), 13–17
I. Yu. Vygodchikova, S. I. Dudov, E. V. Sorina, “External estimation of a segment function by a polynomial strip”, Zh. Vychisl. Mat. Mat. Fiz., 49:7 (2009), 1175–1183; Comput. Math. Math. Phys., 49:7 (2009), 1119–1127
S. I. Dudov, A. B. Konoplev, “Approximation of Continuous Set-Valued Maps by Constant Set-Valued Maps with Image Balls”, Mat. Zametki, 82:4 (2007), 525–529; Math. Notes, 82:4 (2007), 469–473
S. I. Dudov, “Relations between several problems of estimating convex
compacta by balls”, Mat. Sb., 198:1 (2007), 43–58; Sb. Math., 198:1 (2007), 39–53
S. I. Dudov, A. S. Dudova, “On the stability of inner and outer approximations of a convex compact set by a ball”, Zh. Vychisl. Mat. Mat. Fiz., 47:10 (2007), 1657–1671; Comput. Math. Math. Phys., 47:10 (2007), 1589–1602
S. I. Dudov, I. V. Zlatorunskaya, “Best uniform approximation of a convex compact set by a ball in an arbitrary norm”, Zh. Vychisl. Mat. Mat. Fiz., 45:3 (2005), 416–428; Comput. Math. Math. Phys., 45:3 (2005), 399–411
S. I. Dudov, I. V. Zlatorunskaya, “Uniform estimate of a compact convex set by a ball in an arbitrary norm”, Mat. Sb., 191:10 (2000), 13–38; Sb. Math., 191:10 (2000), 1433–1458
S. I. Dudov, “On the generalized gradient of the distance function”, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 61 (1999), 5–14; J. Math. Sci. (New York), 100:6 (2000), 2593–2600
S. I. Dudov, “Subdifferentiability and superdifferentiability of distance functions”, Mat. Zametki, 61:4 (1997), 530–542; Math. Notes, 61:4 (1997), 440–450
S. I. Dudov, “Inner estimation of a convex set by a norm body”, Zh. Vychisl. Mat. Mat. Fiz., 36:5 (1996), 153–159; Comput. Math. Math. Phys., 36:5 (1996), 683–688
S. I. Dudov, “Necessary and sufficient conditions for the maximin of a function of the difference of arguments”, Zh. Vychisl. Mat. Mat. Fiz., 32:12 (1992), 1869–1884; Comput. Math. Math. Phys., 32:12 (1992), 1701–1714
D. V. Prokhorov, S. I. Dudov, A. M. Zakharov, V. B. Poplavskii, V. V. Rozen, S. P. Sidorov, “In memory of Alexandr Yu. Vasiliev”, Izv. Saratov Univ. Math. Mech. Inform., 17:1 (2017), 117–121
2016
34.
M. V. Balashov, O. V. Besov, B. I. Golubov, V. V. Goryainov, V. N. Diesperov, S. I. Dudov, G. E. Ivanov, S. P. Konovalov, R. V. Konstantinov, A. B. Kurzhanskii, S. R. Nasyrov, A. G. Sergeev, V. V. Starkov, V. M. Tikhomirov, M. I. Shabunin, “Evgenii Sergeevich Polovinkin (on his 70th birthday)”, Uspekhi Mat. Nauk, 71:5(431) (2016), 187–190; Russian Math. Surveys, 71:5 (2016), 983–987
2010
35.
D. V. Prokhorov, A. M. Zaharov, S. I. Dudov, “Avgust Petrovich Khromov (on his 75th birthday)”, Izv. Saratov Univ. Math. Mech. Inform., 10:3 (2010), 92–93
2007
36.
D. V. Prokhorov, A. M. Zaharov, S. I. Dudov, “Avgust Petrovich Khromov”, Izv. Saratov Univ. Math. Mech. Inform., 7:2 (2007), 82–84
37.
S. I. Dudov, A. M. Zaharov, D. V. Prokhorov, A. P. Khromov, “Petr Lavrentievich Ulianov”, Izv. Saratov Univ. Math. Mech. Inform., 7:1 (2007), 89–93
Presentations in Math-Net.Ru
1.
Об остром минимуме в задаче чебышевского приближения S. I. Dudov, M. A. Osiptsev XXII International Saratov Winter School
"Contemporary Problems of Function Theory and Their Applications",
dedicated to the 300th anniversary of the Russian Academy of Sciences January 28, 2024 15:30
