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Polovinkin, Evgenii Sergeevich
Polovinkin, Evgenii Sergeevich
Professor
Doctor of physico-mathematical sciences (1987)
Speciality: 01.01.02 (Differential equations, dynamical systems, and optimal control)
Birth date: 1.08.1946
E-mail:
Keywords: optimal control, differential games, convex analysis, strongly convex analysis, differential inclusion, set-valued analysis, nonsmooth analysis.

Subject:

optimal control, differential games, convex analysis, nonsmooth analysis, set-valued maps
   
Main publications:
  1. E. S. Polovinkin, “On the calculation of the polar cone of the solution set of a differential inclusion”, Proc. Steklov Inst. Math., 278 (2012), 169–178  mathnet  crossref  mathscinet  isi  elib  elib  scopus
  2. E. S. Polovinkin, “O nekotorykh svoistvakh proizvodnykh mnogoznachnykh otobrazhenii”, Trudy MFTI, 4:4 (2012), 141–154 http://mipt.ru/science/trudy/trudy_mipt_16/f_gier-arphcxl1tgs  elib
  3. G. Ivanov, E. S. Polovinkin, “A Generalization of the Set Averaging Theorem”, Math. Notes, 92:3 (2012), 369–374  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib  scopus
  4. E. S. Polovinkin, “Teorema suschestvovaniya reshenii differentsialnogo vklyucheniya s psevdo-lipshitsevoi pravoi chastyu”, Nelineinyi mir, 10:9 (2012), 571–578  elib
  5. E. S. Polovinkin, “Integrirovanie po Rimanu mnogoznachnykh otobrazhenii”, Trudy MFTI, 3:1 (2011), 117–126 http://mipt.ru/science/trudy/trudy-9/Pages_from_117-126-arphcxl1tgs.pdf  elib
  6. E. S. Polovinkin, “On construction of bodies of constant width containing a given set”, Proc. Inst. Math. Mech., 269, suppl. 1 (2010), S247–S257  mathnet  crossref  elib  scopus
  7. E. S. Polovinkin, M. V. Balashov, Elementy vypuklogo i silno vypuklogo analiza, 2-e izd., Fizmatlit, Moskva, 2007 , 440 pp., (1-e izd. 2004)
  8. V. K. Zakharov, E. S. Polovinkin, A. D. Yashin, “Matematicheskaya model gosudarstva”, DAN, 413:2 (2007), 158–162  mathnet  zmath  elib
  9. E. S. Polovinkin, S. V. Sidenko, “The addition of subsets to constant width bodies”, Physics and mathematics, Kazan. Gos. Univ. Uchen. Zap. Ser. Fiz.-Mat. Nauki, 148, no. 2, Kazan University, Kazan, 2006, 132–143  mathnet  zmath
  10. E. S. Polovinkin, “O telakh postoyannoi shiriny”, DAN, 397:3 (2004), 313–315  mathnet  mathscinet  zmath
  11. E. S. Polovinkin, G. E. Ivanov, M. V. Balashov, R. V. Konstantinov, A. V. Khorev, “An algorithm for the numerical solution of linear differential games”, Sb. Math., 192:10 (2001), 1515–1542  mathnet  crossref  crossref  mathscinet  zmath  isi  scopus
  12. M. V. Balashov, E. S. Polovinkin, “$M$-strongly convex subsets and their generating sets”, Sb. Math., 191:1 (2000), 25–60  mathnet  crossref  crossref  mathscinet  zmath  isi  scopus
  13. E. S. Polovinkin, “On strongly convex sets and strongly convex functions”, J. Math. Sci. (New York), 100:6 (2000), 2633–2681  mathnet  crossref  mathscinet  zmath  scopus
  14. E. S. Polovinkin, “Obobschenie teorem Karateodori i Kreina-Milmana dlya silno vypuklykh mnozhestv”, DAN, 355:2 (1997), 164–166  mathnet  mathscinet  zmath
  15. E. S. Polovinkin, “Strongly convex analysis”, Sb. Math., 187:2 (1996), 259–286  mathnet  crossref  crossref  mathscinet  zmath  isi  scopus
  16. E. S. Polovinkin, “O vypuklykh i silno vypuklykh approksimatsiyakh mnozhestv”, DAN, 350:3 (1996), 308–311  mathnet  mathscinet  zmath
  17. E. S. Polovinkin, “Necessary conditions for an optimization problem with a differential inclusion”, Proc. Steklov Inst. Math., 211 (1995), 350–361  mathnet  mathscinet  zmath
  18. G. E. Ivanov, E. S. Polovinkin, “On strongly convex differential games”, Differ. Equ., 31:10 (1995), 1603–1612  mathnet  mathscinet  zmath
  19. G. E. Ivanov, E. S. Polovinkin, “Second-order convergence of an algorithm calculating the value of linear differential games”, Dokl. Math., 51:1 (1995), 29–32  mathnet  mathscinet  zmath
  20. E. S. Polovinkin, G. V. Smirnov, “Differentiation of multivalued mappings and properties of solutions of differential inclusions”, Dokl. Math., 33 (1986), 662–666  mathnet  mathscinet  zmath
  21. E. S. Polovinkin, G. V. Smirnov, Differ. Equ., 22 (1986), 660–668  mathnet  mathscinet  zmath
  22. E. S. Polovinkin, G. V. Smirnov, “Time-optimal problem for differential inclusions”, Differ. Equ., 22:8 (1986), 940–952  mathnet  mathscinet  zmath
  23. E. S. Polovinkin, “Stabilnost terminalnogo mnozhestva i optimalnost vremeni presledovaniya v differentsialnykh igrakh”, Differentsialnye uravneniya, 20:3 (1984), 433–446  mathnet  mathscinet  zmath
  24. P. B. Gusyatnikov, E. S. Polovinkin, “O dvukh tipakh operatorov dlya biparametricheskikh uravnenii”, DAN, 254:1 (1980), 20–24  mathnet  mathscinet  zmath
  25. E. S. Polovinkin, “Neavtonomnye differentsialnye igry”, Differentsialnye uravneniya, 15:6 (1979), 1007–1017  mathnet  mathscinet  zmath
  26. E. S. Polovinkin, “Ob antagonisticheskikh igrakh dvukh lits v dinamicheskikh sistemakh.1”, Vestnik Moskovskogo universiteta, seriya: matematika, mekhanika, 1975, no. 1, 30–36  zmath
  27. E. S. Polovinkin, “Ob antagonisticheskikh igrakh dvukh lits v dinamicheskikh sistemakh.2”, Vestnik Moskovskogo universiteta, seriya: matematika, mekhanika, 1975, no. 2, 15–21  zmath
  28. E. S. Polovinkin, Kurs lektsii po teorii funktsii kompleksnogo peremennogo, Fizmatkniga, Moskva, 2003 , 208 pp.
  29. M. I. Shabunin, M. I. Karlov, E. S. Polovinkin, Matematika. Sbornik zadach po teorii funktsii kompleksnogo peremennogo, Binom. Laboratoriya znanii, 2010 , 368 pp.

https://www.mathnet.ru/eng/person8415
List of publications on Google Scholar
https://zbmath.org/authors/ai:polovinkin.e-s
https://mathscinet.ams.org/mathscinet/MRAuthorID/196557

Full list of publications: http://scholar.google.ru/citations?user=FrAYmpUAAAAJ&hl=ru

Publications in Math-Net.Ru Citations
2020
1. 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  mathnet; Russian Math. (Iz. VUZ), 64:5 (2020), 17–30  isi  scopus 1
2019
2. E. S. Polovinkin, “On the continuous dependence of trajectories of a differential inclusion on initial approximations”, Trudy Inst. Mat. i Mekh. UrO RAN, 25:1 (2019),  174–195  mathnet  elib 1
3. E. S. Polovinkin, “Pontryagin's Direct Method for Optimization Problems with Differential Inclusion”, Trudy Mat. Inst. Steklova, 304 (2019),  257–272  mathnet  mathscinet  elib; Proc. Steklov Inst. Math., 304 (2019), 241–256  isi  scopus 2
2018
4. E. S. Polovinkin, “On some properties of vector measures”, Trudy Inst. Mat. i Mekh. UrO RAN, 24:1 (2018),  175–188  mathnet  elib; Proc. Steklov Inst. Math. (Suppl.), 303, suppl. 1 (2018), 183–195  isi  scopus 1
2015
5. E. S. Polovinkin, “Differential inclusions with unbounded right-hand side and necessary optimality conditions”, Trudy Mat. Inst. Steklova, 291 (2015),  249–265  mathnet  elib; Proc. Steklov Inst. Math., 291 (2015), 237–252  isi  scopus 5
2014
6. E. S. Polovinkin, “Subdifferentials for the difference of two convex functions”, Fundam. Prikl. Mat., 19:5 (2014),  167–184  mathnet  mathscinet; J. Math. Sci., 218:5 (2016), 664–677 1
7. E. S. Polovinkin, “On a Consequence of the Schauder Theorem”, Mat. Zametki, 96:6 (2014),  953–954  mathnet  mathscinet  zmath  elib; Math. Notes, 96:6 (2014), 1020–1021  isi  elib  scopus 1
8. E. S. Polovinkin, “On a Counterexample in Analysis”, Mat. Zametki, 95:1 (2014),  123–128  mathnet  mathscinet  elib; Math. Notes, 95:1 (2014), 111–115  isi  elib  scopus
9. E. S. Polovinkin, “On the weak polar cone of the solution set of a differential inclusion with conic graph”, Trudy Inst. Mat. i Mekh. UrO RAN, 20:4 (2014),  238–246  mathnet  mathscinet  elib; Proc. Steklov Inst. Math. (Suppl.), 292, suppl. 1 (2016), 253–261  isi  scopus 2
2013
10. E. S. Polovinkin, “On Relationship between Derivative of Multifunction and Its Support Function”, Izv. Saratov Univ. Math. Mech. Inform., 13:1(1) (2013),  13–21  mathnet  elib
11. E. S. Polovinkin, “Differential inclusions with measurable-pseudo-Lipschitz right-hand side”, Trudy Mat. Inst. Steklova, 283 (2013),  121–141  mathnet  mathscinet  elib; Proc. Steklov Inst. Math., 283 (2013), 116–135  isi  elib 11
2012
12. G. Ivanov, E. S. Polovinkin, “A Generalization of the Set Averaging Theorem”, Mat. Zametki, 92:3 (2012),  410–416  mathnet  mathscinet  zmath  elib; Math. Notes, 92:3 (2012), 369–374  isi  elib  scopus 2
13. E. S. Polovinkin, “On the calculation of the polar cone of the solution set of a differential inclusion”, Trudy Mat. Inst. Steklova, 278 (2012),  178–187  mathnet  mathscinet  elib; Proc. Steklov Inst. Math., 278 (2012), 169–178  isi  elib  scopus 6
2009
14. E. S. Polovinkin, “On construction of bodies of constant width containing a given set”, Trudy Inst. Mat. i Mekh. UrO RAN, 15:4 (2009),  215–225  mathnet  elib; Proc. Steklov Inst. Math. (Suppl.), 269, suppl. 1 (2010), S247–S257  scopus 4
2006
15. E. S. Polovinkin, S. V. Sidenko, “The addition of subsets to constant width bodies”, Kazan. Gos. Univ. Uchen. Zap. Ser. Fiz.-Mat. Nauki, 148:2 (2006),  132–143  mathnet  zmath 3
2001
16. E. S. Polovinkin, G. E. Ivanov, M. V. Balashov, R. V. Konstantinov, A. V. Khorev, “An algorithm for the numerical solution of linear differential games”, Mat. Sb., 192:10 (2001),  95–122  mathnet  mathscinet  zmath; Sb. Math., 192:10 (2001), 1515–1542  isi  scopus 38
2000
17. M. V. Balashov, E. S. Polovinkin, “$M$-strongly convex subsets and their generating sets”, Mat. Sb., 191:1 (2000),  27–64  mathnet  mathscinet  zmath; Sb. Math., 191:1 (2000), 25–60  isi  scopus 44
1999
18. E. S. Polovinkin, “On strongly convex sets and strongly convex functions”, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 61 (1999),  66–138  mathnet  mathscinet  zmath; J. Math. Sci. (New York), 100:6 (2000), 2633–2681 11
1996
19. E. S. Polovinkin, “On convex and strongly convex approximations of sets”, Dokl. Akad. Nauk, 350:3 (1996),  308–311  mathnet  mathscinet  zmath 1
20. E. S. Polovinkin, “Strongly convex analysis”, Mat. Sb., 187:2 (1996),  103–130  mathnet  mathscinet  zmath; Sb. Math., 187:2 (1996), 259–286  isi  scopus 84
1995
21. G. E. Ivanov, E. S. Polovinkin, “Second-order convergence of an algorithm calculating the value of linear differential games”, Dokl. Akad. Nauk, 340:2 (1995),  151–154  mathnet  mathscinet  zmath; Dokl. Math., 51:1 (1995), 29–32 6
22. G. E. Ivanov, E. S. Polovinkin, “On strongly convex differential games”, Differ. Uravn., 31:10 (1995),  1641–1648  mathnet  mathscinet  zmath; Differ. Equ., 31:10 (1995), 1603–1612 9
23. E. S. Polovinkin, “Necessary conditions for an optimization problem with a differential inclusion”, Trudy Mat. Inst. Steklov., 211 (1995),  387–400  mathnet  mathscinet  zmath; Proc. Steklov Inst. Math., 211 (1995), 350–361 5
1986
24. E. S. Polovinkin, G. V. Smirnov, “Differentiation of multivalued mappings and properties of solutions of differential inclusions”, Dokl. Akad. Nauk SSSR, 288:2 (1986),  296–301  mathnet  mathscinet  zmath; Dokl. Math., 33 (1986), 662–666 4
25. E. S. Polovinkin, G. V. Smirnov, “Time-optimal problem for differential inclusions”, Differ. Uravn., 22:8 (1986),  1351–1365  mathnet  mathscinet  zmath; Differ. Equ., 22:8 (1986), 940–952 8
26. E. S. Polovinkin, G. V. Smirnov, “An approach to differentiation of multivalued mappings, and necessary conditions for optimality of solutions of differential inclusions”, Differ. Uravn., 22:6 (1986),  944–954  mathnet  mathscinet  zmath; Differ. Equ., 22 (1986), 660–668 8
1984
27. E. S. Polovinkin, “Stability of a terminal set and optimality of pursuit time in differential games”, Differ. Uravn., 20:3 (1984),  433–446  mathnet  mathscinet 9
1983
28. E. S. Polovinkin, “The integration of multivalued mappings”, Dokl. Akad. Nauk SSSR, 271:5 (1983),  1069–1074  mathnet  mathscinet  zmath; Dokl. Math., 28 (1983), 223–228 6
1980
29. P. B. Gusyatnikov, E. S. Polovinkin, “On two types of operators for biparametric equations”, Dokl. Akad. Nauk SSSR, 254:1 (1980),  20–24  mathnet  mathscinet  zmath
30. P. B. Gusyatnikov, E. S. Polovinkin, “A linear differential game with a simple matrix”, Differ. Uravn., 16:8 (1980),  1360–1369  mathnet  mathscinet
1979
31. E. S. Polovinkin, “Nonautonomous differential games”, Differ. Uravn., 15:6 (1979),  1007–1017  mathnet  mathscinet  zmath 3
2004
32. A. V. Arutyunov, A. P. Buslaev, È. M. Galeev, M. L. Gol'dman, V. B. Demidovich, A. G. Kusraev, S. S. Kutateladze, G. G. Magaril-Il'yaev, K. Yu. Osipenko, E. S. Polovinkin, “Vladimir Mikhaĭlovich Tikhomirov (on the occasion of his seventieth birthday)”, Vladikavkaz. Mat. Zh., 6:4 (2004),  3–6  mathnet  mathscinet  zmath 1

Presentations in Math-Net.Ru
1. On necessary conditions in the Mayer problem with differential inclusion
Evgenii Polovinkin
International conference "Systems Analysis: Modeling and Control" in memory of Academician A. V. Kryazhimskiy
June 1, 2018 11:30   
2. Optimal control of unbounded differential inclusions
E. S. Polovinkin
International conference "Dynamical Systems: Inverse Problems, Stability and Control Processes" dedicated to the 80th birthday of Yu. S. Osipov
September 22, 2016 16:30   
3. Differentiation of set-valued maps and direct method for studying the problems with differential inclusions
E. S. Polovinkin
Conference "Optimal Control and Applications" dedicated to the 105th anniversary of Lev Semenovich Pontryagin
September 24, 2013 16:10   

Organisations
 
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