Đại học Tôn Đức Thắng
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GS. TS. ALEXANDER KRUGER

 

 

Thông tin chung
Alex

GS. TS. ALEXANDER KRUGER

Tiến sĩ 1981

Nghiên cứu viên cao cấp

krugeralexander@tdtu.edu.vn
  1. Quá trình đàotạovà hoạt động khoa học
  2. Quá trình đào tạo
  • 1981: Tiến sĩ Toán học, Đại học Quốc gia Belarus, Minsk, Belarus
  • 1975: Thạc sĩ Toán ứng dụng, Đại học Quốc gia Belarus, Minsk, Belarus
  1. Quá trình hoạt động chuyên môn
  • 2023-nay:  Nghiên cứu viên cao cấp, Khoa Toán-Thống kê, Trường Đại học Tôn Đức Thắng, Việt Nam
  • 2021-nay: Trường khoa học, Đại học RMIT, Melbourne, Australia. GS liên kết
  • 2020-nay: Trường khoa học kỹ thuật, CNTT và vật lý, Đại học liên đoàn Úc. GS danh dự
  • 2014 - 2020: Trung tâm tin học và tối ưu ứng dụng, Đại học liên đoàn Úc. Giám đốc nghiên cứu
  • 2003 - 2020: Trường khoa học kỹ thuật, CNTT và vật lý, Đại học liên đoàn Úc. GS (từ 2019)
  • 1995 - 2003: Bộ môn  Toán-Tin, Viện lao động và quan hệ XH quốc tế, Minsk, Belarus. GS
  • 1987 - 1995: Viện NCKH về  kinh tế và tin học, Minsk, Belarus. Trưởng nhóm nghiên cứu
  • 1982 - 1987: PTO “Avtotranssystema”, Minsk, Belarus. Kỹ sư cao cấp
  • 1979 - 1981: Đại học Quốc gia Belarus, Minsk, Belarus. Kỹ sư trẻ
  1. Lĩnh vực nghiên cứu
  • Tối ưu
  • Giải tích phi tuyến
  1. 4. Chương trình, đề tài nghiên cứu (làm chủ nhiệm)

+ 2016 – 2022: DP160100854. Stability of generalised equations and variational systems, ARC

+ 2011 – 2016: DP110102011. Stationarity and regularity in variational analysis with applications to optimization, ARC

+ 1999 – 2001: INTAS 97-1050. Convex analysis and extremal problems, INTAS

+ 1999 – 2001: INTAS 9731854. Network for developing theory, methods and applications of nonsmooth analysis and optimization, INTAS

  1. Hướng dẫn luận án

- 7 tiến sĩ và 1 thạc sĩ

  1. Công bố Khoa học
  2. H. Gfrerer, A. Y. Kruger.Radius theorems for subregularity in infinite dimensions, Comp. Optim. Appl., published online 3/01/2023. DOI: 10.1007/s10589-022-00431-6
  3. A. M. Bagirov, R. S. Burachik, A. Y. Kruger, J. E. Martinez-Legaz, X. Q. Yang.EDITORIAL: Special issue dedicated to the 80th birthday of Professor Alexander Rubinov, Optimization, 71 (2022), no. 4, 775-778. DOI: 10.1080/02331934.2022.2057066 
  4. Hoa T. Bui, R. S. Burachik, A. Y. Kruger, D. T. Yost.Zero duality gap conditions via abstract convexity, Optimization, 71 (2022), no. 4, 811-847. DOI: 10.1080/02331934.2021.1910694
  5. Hoa T. Bui, A. Y. Kruger.Extremal principle: Nonlinear characterizations of non-intersection properties, Optimization, 71 (2022), no. 1, 165-196. DOI: 10.1080/02331934.2021.1901899
  6. N. D. Cuong, A. Y. Kruger.Error bounds revisited, Optimization, 71 (2022), no. 4, 1021-1053. DOI: 10.1080/02331934.2022.2032695 
  7. A. Y. Kruger, M. A. López, X. Q. Yang, J. Zhu. Isolated calmness and sharp minima via Hölder graphical derivatives, Set-Valued Var. Anal., 30(2022), no. 4, 1423–1441. DOI: 10.1007/s11228-022-00628-1
  8. A. Y. Kruger, P. Mehlitz.Optimality conditions, approximate stationarity, and applications – a story beyond Lipschitzness, ESAIM: Control, Optimisation and Calculus of Variations 28 (2022), Article Number 42. DOI: 10.1051/cocv/2022024
  9. M. Abbasi, A. Y. Kruger, M. A. Théra.Gateaux differentiability revisited, Appl. Math. Optim. 84 (2021), no. 3, 3499-3516.
  10. M. Abbasi, A. Y. Kruger, M. A. Théra.Enlargements of the Moreau-Rockafellar subdifferential, Set-Valued Var. Anal. 29 (2021), no. 3, 701-719.
  11. N. D. Cuong, A. Y. Kruger.Characterizations of uniform regularity of set-valued mappings, J. Nonsmooth Anal. Optim. 2 (2021), 6599.
  12. N. D. Cuong, A. Y. Kruger.Primal necessary characterizations of transversality properties, Positivity 25 (2021), no. 2, 531-558.
  13. N. D. Cuong, A. Y. Kruger.Transversality properties: Primal sufficient conditions, Set-Valued Var. Anal. 29 (2021), no. 2, 221-256.
  14. Hoa T. Bui, N. D. Cuong, A. Y. Kruger. Geometric and metric characterizations of transversality properties, Vietnam J. Math. 48(2020), no. 2, 277-297.
  15. N. D. Cuong, A. Y. Kruger. Nonlinear transversality properties of collections of sets: Dual space necessary characterizations, J. Convex Anal. 27(2020), no. 1, 287-308.
  16. N. D. Cuong, A. Y. Kruger.Dual sufficient characterizations of transversality properties, Positivity 24 (2020), no. 5, 1313-1359.
  17. A. L. Dontchev, H. Gfrerer, A. Y. Kruger, J. V. Outrata.The radius of metric subregularity, Set-Valued Var. Anal. 28 (2020), no. 3, 451-473.
  18. Hoa T. Bui, A. Y. Kruger. Extremality, stationarity and generalized separation of collections of sets, J. Optimization Theory Appl. 182(2019) no. 1, 211-264.
  19. R. Cibulka, M. Fabian, A. Y. Kruger. On semiregularity of mappings, J. Math. Anal. Appl. 473(2019) no. 2, 811-836.
  20. A. Y. Kruger, M. A. López, X. Q. Yang, J. Zhu. Hölder error bounds and Hölder calmness with applications to convex semi-infinite optimization, Set-Valued Var. Anal. 27(2019) no. 4, 995-1023.
  21. Hoa T. Bui, A. Y. Kruger.About extensions of the extremal principle, Vietnam J. Math. 46 (2018), no. 2, 215-242.
  22. R. Cibulka, A. L. Dontchev, A. Y. Kruger.Strong metric subregularity of mappings in variational analysis and optimization, J. Math. Anal. Appl. 457 (2018), no. 2, 1247-1282.
  23. A. Y. Kruger.About intrinsic transversality of pairs of sets, Set-Valued Var. Anal., 26 (2018), no. 1, 111-142.
  24. A. Y. Kruger, M. A. López, M. A. Théra. Perturbation of error bounds, Math. Program, Ser. B, 168(2018), no. 1-2, 533-554.
  25. A. Y. Kruger, D. R. Luke, N. H. Thao.Set regularities and feasibility problems, Math. Program., ser. B, 168 (2018), no. 1-2, 279-311.
  26. A. Y. Kruger, D. R. Luke, N. H. Thao.About subtransversality of collections of sets, Set-Valued Var. Anal., 25 (2017), no. 4, 701-729.
  27. A. Y. Kruger, S. Plubtieng, T. Seangwattana.Borwein–Preiss vector variational principle, Positivity, 21 (2017), no. 4, 1273-1292.
  28. A. Y. Kruger.Nonlinear metric subregularity, J. Optim. Theory Appl., 171 (2016), no. 3, 820-855.
  29. A. Y. Kruger, S. Plubtieng, T. Seangwattana.Borwein–Preiss variational principle revisited, J. Math. Anal. Appl. 435 (2016), no. 2, 1183-1193.
  30. A. Y. Kruger, N. H. Thao.Regularity of collections of sets and convergence of inexact alternating projections, J. Convex Anal., 23 (2016), no. 3, 823-847.
  31. P. Q. Khanh, A. Y. Kruger, N. H. Thao.An induction theorem and nonlinear regularity models, SIAM J. Optim., 25 (2015) no. 4, 2561-2588.
  32. A. Y. Kruger.Error bounds and metric subregularity, Optimization, 64 (2015), no. 1, 49-79.
  33. A. Y. Kruger.Error bounds and Hölder metric subregularity, Set-Valued Var. Anal., 23 (2015) no. 4, 705-736.
  34. A. Y. Kruger, N. H. Thao.Quantitative characterizations of regularity properties of collections of sets, J. Optim. Theory Appl., 164 (2015), no. 1, 41-67.
  35. L. Q. Anh, T. Q. Duy, A. Y. Kruger, N. H. Thao.Well-posedness for lexicographic vector equilibrium problems, Constructive Nonsmooth Analysis and Related Topics (Panos M. Pardalos, Vladimir Demyanov, and Mikhail Batsyn, eds.), Springer-Verlag, Berlin, 2014, 157-172.
  36. L. Q. Anh, A. Y. Kruger, N. H. Thao. On Hölder calmness of solution mappings in parametric equilibrium problems, TOP, 22(2014), no.1, 331-342.
  37. M. J. Cánovas, A. Y. Kruger, M. A. López, J. Parra, M. A. Théra.Calmness modulus of linear semi-infinite programs, SIAM J. Optim., 24 (2014), no. 1, 29-48.
  38. A. Y. Kruger, L. Minchenko, J. V. Outrata.On relaxing the Mangasarian-Fromovitz constraint qualification, Positivity, 18 (2014), no. 1, 171-189.
  39. A. Y. Kruger, N. H. Thao.About [q]-regularity properties of collections of sets, J. Math. Anal. Appl., 416 (2014), no. 2, 471-496.
  40. G.-W. Weber, A. Y. Kruger, J. E. Martínez-Legaz, B. S. Mordukhovich, L. Sakalauskas.EDITORIAL: Special Issue on recent advances in continuous optimization on the occasion of the 25th European conference on Operational Research (EURO XXV 2012), Optimization, 63 (2014), no. 1, 1-5.
  41. R. Henrion, A. Y. Kruger, J. V. Outrata.Some remarks on stability of generalized equations, J. Optim. Theory Appl., 159 (2013), no. 3, 681-697.
  42. A. Y. Kruger, N. H. Thao.About uniform regularity of collections of sets, Serdica Math. J., 39 (2013), no. 3-4, 287-312.
  43. E. Bednaczuk and A. Y. Kruger.Error bounds for vector-valued functions: necessary and sufficient conditions, Nonlinear Anal., 75 (2012), no. 3, 1124-1140.
  44. E. Bednaczuk and A. Y. Kruger.Error bounds for vector-valued functions on metric spaces, Vietnam J. Math., 40 (2012), no. 2-3, 165-180.
  45. M. Fabian, R. Henrion, A. Y. Kruger, J. V. Outrata.About error bounds in metric spaces, Operations Research Proceedings 2011. Selected Papers of the International Conference on Operations Research (OR 2011), August 30 – September 2, 2011, Zurich, Switzerland (Diethard Klatte, Hans-Jacob Lüthi, and Karl Schmedders, eds.), Springer-Verlag, Berlin, 2012, 33-38.
  46. D. Klatte, A. Y. Kruger,and B. Kummer. From convergence principles to stability and optimality conditions, J. Convex Anal., 19 (2012), no. 4, 1043-1072.
  47. A. Y. Kruger.Comments on: Stability in linear optimization and related topics. A personal tour, TOP, 20 (2012), no. 2, 255-257.
  48. A. Y. Kruger andM. A. López, Stationarity and regularity of infinite collections of sets, J. Optim. Theory Appl., 154 (2012), no. 2, 339-369.
  49. A. Y. Kruger andM. A. López, Stationarity and regularity of infinite collections of sets. Applications to infinitely constrained optimization, J. Optim. Theory Appl., 155 (2012), no. 2, 390-416.
  50. H. V. Ngai, A. Y. Kruger, M. Théra.Slopes of multifunctions and extensions of metric regularity, Vietnam J. Math., 40 (2012), no. 2-3, 355-369.
  51. T. D. Chuong, A. Y. Kruger, and J.-C. Yao.Calmness of efficient solution maps in parametric vector optimization, J. Global Optim., 51 (2011), no. 4, 677-688.
  52. A. Y. Kruger, H. Van Ngai, and M. Théra. Stability of error bounds for convex constraint systems in Banach spaces, SIAM J. Optim., 20(2010), no. 6, 3280-3296.
  53. M. Fabian, R. Henrion, A. Kruger, and J. OutrataError bounds: necessary and sufficient conditions, Set-Valued Var. Anal., 18 (2010), no. 2, 121-149.
  54. H. Van Ngai, A. Y. Kruger, and M. Théra. Stability of error bounds for semi-infinite convex constraint systems, SIAM J. Optim., 20(2010), no. 4, 2080-2096.
  55. A. Y. Kruger.About stationarity and regularity in variational analysis, Taiwan. J. Math., 13 (2009) no. 6a, 1737-1785.
  56. A. V. Dmitruk andA. Y. Kruger. Extensions of metric regularity, Optimization, 58 (2009), no. 5, 561-584.
  57. A. Y. Kruger.Nonsmooth analysis: Fréchet subdifferentials, Encyclopaedia of Optimization, Second edition (Christodoulos A. Floudas and Panos M. Pardalos, eds.), Springer-Verlag, Boston, 2009, 2651-2658.
  58. A. Y. Kruger.Nonsmooth analysis: Weak stationarity, Encyclopaedia of Optimization, Second edition (Christodoulos A. Floudas and Panos M. Pardalos, eds.), Springer-Verlag, Boston, 2009, 2658-2664.
  59. A. V. Dmitruk andA. Y. Kruger. Metric regularity and systems of generalized equations, J. Math. Anal. Appl. 342 (2008), no. 2, 864-873.
  60. R. Henrion, A. Y. Kruger, and J. Outrata.Boris Mordukhovich, the never tiring traveller, celebrates his sixtieth birthday, Set-Valued Anal. 16 (2008), no. 2-3, 125-127.
  61. A. Y. Kruger. About extremality, stationarity and regularity, Dynamical Systems: Stability, Control, Optimization. Minsk, 2008, 31-33.
  62. J. Ugon, S. Kouhbor, M. Mammadov, A. Rubinov andA. Y. Kruger. Facility location via continuous optimization with discontinuous objective functions, ANZIAM J. 48 (2007), 315-325.
  63. A. Y. Kruger.Stationarity and regularity of real-valued functions, Appl. Comput. Math. 5 (2006), no.1, 79-93.
  64. A. Y. Kruger.Stationarity and regularity concepts for set systems, IFIP International Federation for Information Processing, Vol. 202, Systems, Control, Modeling and Optimization, F. Ceragioli, A. Dontchev, H. Furuta, K. Marti, L. Pandolfi (Editors), Boston: Springer, 2006, 205-214.
  65. A. Y. Kruger.About regularity of collections of sets, Set-Valued Anal. 14 (2006), 187-206.
  66. A. Y. Kruger.Stationarity and regularity of set systems, Pac. J. Optim., 1 (2005), 101-126.
  67. A. Y. Kruger,S. A. Chernishova, and L. G. Shipulina. Operating System MS Windows 2000 Professional, Minsk, 2005. (In Russian). ISBN 985-6741-44-0.
  68. A. Y. Kruger.Weak stationarity: eliminating the gap between necessary and sufficient conditions, Optimization, 53 (2004), 147-164.
  69. A. Y. Kruger.About stationarity and regularity of real-valued functions, Proceedings of the 6th International Conference on Optimization: Techniques and Applications (ICOTA6), Alex Rubinov & Moshe Sniedovich (Editors), Ballarat, December 2004, Article index number 199, 6 pp. University of Ballarat, 2004, ISBN 1876851155.
  70. A. Y. Kruger.On Fréchet subdifferentials, J. Math. Sci., 116 (2003), 3325-3358.
  71. A. Y. Kruger.Strict (ε,δ)-subdifferentials and extremality conditions, Optimization, 51 (2002), 539-554.
  72. A. Y. Kruger,A.Y. Turin, S.A. Chernishova. Microsoft Excel for Windows. Laboratory Works, Minsk, 2001. (In Russian). ISBN 985-6464-32-3.
  73. A. Y. Kruger.Strict (ε,δ)-semidifferentials and extremality conditions, U.S.-Ukrainian Workshop: Recent Advances in Non-Differentiable Optimization, Kyiv, 2000, 24.
  74. A. Y. Kruger.Strict (ε,δ)-semidifferentials and extremality of sets and functions, Dokl. Nat. Akad. Nauk Belarus, 44 (2000), no.2, 21-24 (In Russian).
  75. A. Y. Kruger.On necessary and sufficient extremality conditions, Int. Conf. Dynamical Systems: Stability, Control, Optimization. Vol.2, Minsk, 1998, 165-168.
  76. A. Y. Kruger.About extremality of sets systems, Dokl. Nat. Akad. Nauk Belarus, 42 (1998), no.1, 24-28 (In Russian).
  77. A. Y. Kruger.Strict ε-semidifferentials and extremality conditions, Dokl. Akad. Nauk Belarus, 41 (1997), no.3, 21-26 (In Russian).
  78. A. Y. Kruger.On calculus of strict ε-semidifferentials, Dokl. Akad. Nauk Belarus, 40 (1996), no.4, 34-39 (In Russian).
  79. A. Y. Kruger.Strict ε-semidifferentials and differentiating set-valued mappings, Dokl. Akad. Nauk Belarus, 40 (1996), no.6, 38-43 (In Russian).
  80. A. Y. Kruger.On differentiating nonconvex functions, Nonsmooth Analysis and its Applications to Mathematical Economics, Baku, 1991, 25 (In Russian).
  81. A. Y. Kruger.On necessary and sufficient extremality conditions in nonsmooth problems, Methods of Mathematical Programming and Software, Sverdlovsk, 1989, 139-140 (In Russian).
  82. A. Y. Kruger and B. S. Mordukhovich.Generalized differentials and conditions of an extremum in problems of nonsmooth optimization, Optimization Methods in Economics & Mathematical Modeling, Moscow, 1988, 134-157 (In Russian).
  83. A. Y. Kruger.On necessary and sufficient extremality conditions, Problems of Theoretical Cybernetics, Part 1, Gorky, 1988, 185.
  84. A. Y. Kruger.A covering theorem for set-valued mappings, Optimization, 19 (1988), 763-780.
  85. A. Y. Kruger.On calculus formulas for ε-semidifferentials, School on the Theory of Operators in Functional Spaces, Chelyabinsk, 1986, 54 (In Russian).
  86. A. Y. Kruger.Covering theorem for set-valued mappings, Minsk, 1985. 45 pp. Deposited in VINITI no. 4613-85 (In Russian).
  87. A. Y. Kruger.On necessary optimality conditions of an extremum in problems of nondifferentiable programming, VII All-Union Conf. on Problems of Theoretical Cybernetics, Part. 2, Irkutsk, 1985, 66-67 (In Russian).
  88. A. Y. Kruger.Covering theorem and optimal control of nonsmooth systems, V All-Union Conf. on Control in Mechanical Systems, Khazan, 1985, 45 (In Russian).
  89. A. Y. Kruger.Generalized differentials of nonsmooth functions and necessary conditions for an extremum, Sibirskii Matem. Zh., 26 (1985), no. 3, 78-90 (In Russian). English translation: Siberian Math. J., 26 (1985), 370-379.
  90. A. Y. Kruger.Properties of generalized differentials, Sibirskii Matem. Zh., 26 (1985), no. 6, 54-66 (In Russian).
    English translation: Siberian Math. J., 26 (1985), 822-832.
  91. A. Y. Kruger.On necessary optimality conditions in nonsmooth problems, III Conf. of Young Scientists of Transcaucasian Republics on Automatic Control, Tbilisi, 1982, 48-50 (In Russian).
  92. A. Y. Kruger.On characterizing the covering property for nonsmooth operators, School on the Theory of Operators in Functional Spaces, Minsk, 1982, 94-95 (In Russian).
  93. A. Y. Kruger.ε-semidifferentials and ε-normal elements, Minsk, 1981. 76 pp. Deposited in VINITI no. 1331-81 (In Russian).
  94. A. Y. Kruger.Generalized differentials of nonsmooth functions, Minsk, 1981. 67 pp. Deposited in VINITI no. 1332-81 (In Russian).
  95. A. Y. Kruger.Necessary conditions of an extremum in problems of nonsmooth optimization, Minsk, 1981. 55 pp. Deposited in VINITI no. 1333-81 (In Russian).
  96. A. Y. Kruger andB. S. Mordukhovich. Generalized normals and derivatives and necessary conditions of an extremum in problems of nondifferentiable programming. I, Minsk, 1980. 49 pp. Deposited in VINITI no. 408-80 (In Russian).
  97. A. Y. Kruger andB. S. Mordukhovich. Generalized normals and derivatives and necessary conditions of an extremum in problems of nondifferentiable programming. II, Minsk, 1980. 59 pp. Deposited in VINITI no. 494-80 (In Russian).
  98. A. Y. Kruger andB. S. Mordukhovich. Extremal points and the Euler equation in nonsmooth optimization problems, Dokl. Akad. Nauk BSSR, 24 (1980), no. 8, 684-687 (In Russian).
  99. A. Y. Kruger.About the generalized differentials, V Rep. Conf. of Mathematicians of Belarus, Vol. II, Grodno, 1980, 117-118 (In Russian).
  100. A. Y. Kruger andB. S. Mordukhovich. New necessary optimality conditions in problems of nondifferentiable programming, Numerical Methods of Nonlinear Programming, Kharkov, 1979, 116-119 (In Russian).
  101. A. Y. Kruger.On necessary optimality conditions in nonsmooth problems of optimal control, Optimal Control in Mechanical Systems, Vol. II, Kiev, 1979, 38-39 (In Russian).
  102. A. Y. Kruger.Necessary conditions for an extremum in problems of nonconvex programming in a normed linear space, Minsk, 1978. 26 pp. Deposited in VINITI no. 943-78 (In Russian).
  103. A. Y. Kruger andB. S. Mordukhovich. Minimization of nonsmooth functionals in problems of optimal control, Izvestia Akad. Nauk SSSR. Tech. Kybernetyka, 1978, no. 4, 176-182 (In Russian).
    English translation: Engrg. Cybernetics, 1978, no. 4, 126-133.
  104. A. Y. Kruger.Local approximations of sets in linear topological spaces, School on the Theory of Operators in Functional Spaces, Minsk, 1978, 73-74 (In Russian).
  105. A. Y. Kruger.Necessary conditions for weak minimum in the generalized problem of Boltza, Vestn. Belorus. Univ., Ser. 1, (1978), no. 2, 20-23 (In Russian).
  106. A. Y. Kruger.Some theorems on closures of functions with applications to subdifferential calculus, Izvestia Akad. Nauk BSSR, Ser. Phys.-Mat. Nauk, (1978), no. 4, 29-33 (In Russian).
  107. A. Y. Kruger.Subdifferentials of nonconvex functions and generalized directional derivatives, Minsk, 1977. 39 pp. Deposited in VINITI no. 2661-77 (In Russian).
  108. A. Y. Kruger.A maximum principle in problems of minimization of functionals of intermediate points of a dynamical system, Vestn. Belorus. Univ., Ser. 1, (1977), no. 2, 75-78 (In Russian).
  109. A. Y. Kruger.Generalized directional derivatives and necessary conditions of an extremum in nonconvex mathematical programming problems, IV All-Union Conf. on Problems of Theoretical Cybernetics, Novosibirsk, 1977, 60-62 (In Russian).
  110. B.S. Mordukhovich and A. Y. Kruger.Necessary optimality conditions in a problem of terminal control with nonfunctional constraints, Dokl. Akad. Nauk BSSR, 20 (1976), no. 12, 1064-1067 (In Russian).
  111. A. Y. Kruger.On a problem of seeking of a function root, Vestn. Belorus. Univ., Ser. 1, (1976), no. 1, 3-6 (In Russian).
  112. A. Y. Kruger.About optimal search of a function root, Vestn. Belorus. Univ., Ser. 1, (1975), no. 3, 3-4 (In Russian).

 

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