Bui Trong Kien
Doctor

Department of Optimization and Control Theory
Research interests: Nonlinear and Variational Analysis, Optimal Control, Partial Differential Equations


Address
Office: Building A5, Room 113
Tel: +84 (02)4 37563474/ 113
Email: btkien AT math.ac.vn

Born in  Ninh Binh Province, Vietnam


Education and academic degrees:
1993: Bachelor science degree in math
2003:  Doctoral degree in math  2003


Positions:

  • Lecturer at Hoa Lu University, Ninh Binh, Vietnam (1994-2003)
  • Lecturer at National University of Civil Engineering, Hanoi, Vietnam (2003-2012)
  • Researcher at Department of Optimization and Control Theory, Institute of Mathematics, Vietnam Academy of Science and Technology, Hanoi, Vietnam (2012-up to now)
  • Postdoctoral fellow at Department of Applied Mathematics, National Sun-Yat sen University, Taiwan (2005-2008)
  • Postdoctoral fellow at Department of  Mathematics,  Pukyong National University,  Republic of Korea (2008-2009)
  • Experienced researcher of the Alexander von Humboldt Foudation at Department of Mathematics, Duisburg-Essen University, Federal Republic of Germany (2012-2014).


Research areas:  Variational Analysis, Nonlinear Analysis, Variational Inequality, Optimal Control, Partial Differential Equation

 

PUBLICATIONS

List of publications in MathSciNet

List of recent publications
1Huynh Khanh, Bui Trong Kien, On the regularity of multipliers and second-order optimality conditions of KKT-type for semilinear parabolic control problems, Journal of Mathematical Analysis and Applications Volume 538, Issue 1, 1 October 2024, 128436, (SCI-E, Scopus)
2Bui Trong Kien, Arnd Rösch, Nguyen Hai Son, Nguyen Van Tuyen , FEM for semilinear elliptic optimal control with nonlinear and mixed constraints, Journal of Optimization Theory and Applications 197 (2023), 130-173 2023, (SCI-E, Scopus).
3Bui Trong Kien, N. Q. Tuan, Error Estimates for Approximate Solutions toSeminlinear Elliptic Optimal Control Problems with Nonlinear and Mixed Constraints, Numerical Functional Analysis and Optimization, 43 (2022), 1672-1706, (SCI-E, Scopus).
4T. D. Binh, Bui Trong Kien, X. Qin, C.-F. Wen, Regularity of multipliers in second-order optimality conditions for semilinear elliptic control problems, Applicable Analysis: An International Journal, Volume 101, 2022, 5504-5516, (SCI-E, Scopus).
5Bui Trong Kien, V. E. Fedorov, Ta Duy Phuong, Optimal Control Problems Governed by Fractional Differential Equations with Control Constraints, SIAM Journal on Control and OptimizationVol. 60, No. 3, pp. 1732–1762, 2022.
6M. V. Plekhanova, G. D. Baibulatova, Bui Trong Kien, Distributed control for semi-linear equations with Gerasimove- Caputo derivatives, CBΦY Mathematical, 28 (20221), 2
7Bui Trong Kien, Nguyen Thi Thu Huong, Xiaolong Qin, Ching-Feng Wen, Jen-Chih Yao, Regularity of solutions to a distributed and boundary optimal control problem governed by semilinear elliptic equations, Journal of Mathematical Analysis and Appplications, 495 (2021), 124694, (SCI-E, Scopus).
8Bui Trong Kien, Nguyen Quoc Tuan, Ching-Feng Wen, Jen-Chih Yao , L^{\infty} -Stability of a Parametric Optimal Control Problem Governed by Semilinear Elliptic Equations, Applied Mathematics & Optimization volume 84, pages 849–876 (2021), (SCI-E, Scopus).
9Bui Trong Kien, Xiaolong Qin, Ching-Feng Wen, Jen-Chih Yao, Second-Order Optimality Conditions for Multiobjective Optimal Control Problems with Mixed Pointwise Constraints and Free Right End Point, SIAM Journal on Control and Optimization, 58 (2020), no. 4, 2658–2677, (SCI-E, Scopus).
10V.E. Fedorov, Ta Duy Phuong, Bui Trong Kien, K.V. Boyko, E.M. Izhberdeeva, A class of distributed order semilinear equations in banach spaces, Chelyabinsk Physical and Mathematical Journal 5 No. 3 (2020), 342-351.
11Bui Trong Kien, Second-Order Optimality Conditions and Solution Stability to Optimal Control Problems Governed by Stationary Navier-Stokes Equations, Acta Mathematica Vietnamica, 44 (2019), Issue 2, pp 431–448, Scopus.
12Bui Trong Kien, Jen Chih Yao, Semicontinuity of the solution set to a parametric optimal control problem, Applied Analysis and Optimization 2 (2018), 93--116.
13Bui Trong Kien, N. V. Tuyen, J.- C. Yao, Second-order KKT optimality conditions for multi-objective optimal control problems, SIAM Journal on Control and Optimization, 56(2018), 4069--4097, SCI(-E); Scopus.
14Bui Trong Kien, Jen Chih Yao, Local stability of solutions to parametric semilinear elliptic optimal control problems, Applied Analysis and Optimization 1 (2017), 361--379.
15Bui Trong Kien, A. Rösch, D. Wachsmuth, Pontryagin’s Principle for Optimal Control Problem Governed by 3D Navier–Stokes Equations, Journal of Optimization Theory and Applications, 173 (2017), 30–55, SCI(-E); Scopus.
16Bui Trong Kien, V. H. Nhu, N. H. Son, Second-Order Optimality Conditions for a Semilinear Elliptic Optimal Control Problem with Mixed Pointwise Constraints, Set-Valued and Variational Analysis 25 (2017) 177–210, SCI(-E); Scopus.
17N. H. Chieu, Bui Trong Kien, N. T. Toan, Further results on subgradients of the value function to a parametric optimal control problem, Journal of Optimization Theory and Applications, 168 (2016), 785--801, SCI(-E); Scopus.
18N. H. Son, Bui Trong Kien, A. Rösch, Second-Order Optimality Conditions for Boundary Control Problems with Mixed Pointwise Constraints, SIAM Journal on Optimization, 26(2016), 1912–1943, SCI(-E); Scopus.
19Bui Trong Kien, Gue Myung Lee, Nguyen Hai Son, First- and Second-Order Necessary Optimality Conditions for Optimal Control Problems Governed by Stationary Navier–Stokes Equations with Pure State Constraints, Vietnam Journal of Mathematics 44 (2016) 103-131,Scopus.
20Bui Trong Kien, V. H. Nhu, A. Rösch, Second-order necessary optimality conditions for a class of optimal control problems governed by partial differential equations with pure state constraints, Journal of Optimization Theory and Applications 165 (2015), 30–61, SCI(-E), Scopus.
21Bui Trong Kien, V.H. Nhu, A. Rösch, Lower semicontinuity of the solution map to a parametric elliptic optimal control problem with  with mixed pointwise constraints. Optimization, 64 (2015), 1219-1238, SCI(-E), Scopus.
22Bui Trong Kien, Nhu, V. H, Second-order necessary optimality conditions for a class of semilinear elliptic optimal control problems with mixed pointwise constraints. SIAM Journal on Control and Optimization 52 (2014), 1166–1202, SCI(-E); Scopus.
23Bui Trong Kien, V. N. Nhu and N. H. Anh, Holder continuity of the solution map to an elliptic optimal control problem with mixed constraints, Taiwanese Journal of Mathematics, 17 (2013), 1245 - 1266, SCI(-E); Scopus.
24Bui Trong Kien, Wong, N.-C.; Yao, J.-C., Necessary conditions for multiobjective optimal control problems with state constraints. Dyn. Contin. Discrete Impuls. Syst. Ser. B Appl. Algorithms 19 (2012), 431–446.
25Bui Trong Kien, N. T. Toan, M. M. Wong and J. C. Yao, Lower semicontinuity of the solution set to a parametric optimal control problem,  SIAM Journal on Control and Optimization, 50 (2012), 2889 -- 2906, SCI(-E); Scopus.
26Bui Trong Kien, G.M. Lee, An existence theorem for generalized variational inequalities with discontinuous and pseudomonotone operators. Nonlinear Anal: Theory, Methods & Applications 74 (2011), 1495–1500.
27Nguyen Thi Toan, Bui Trong Kien, Continuity properties of the solution map to a parametric discrete optimal control problem. J. Nonlinear Convex Anal. 12 (2011), no. 3, 635–650.
28Nguyen Thi Toan, Bui Trong Kien, Subgradients of the value function to a parametric optimal control problem. Set-Valued Var. Anal. 18 (2010), 183–203.
29Bui Trong Kien, N. Q. Huy, N. C. Wong, On the solution existence of generalized vector quasi-equilibrium problems with discontinuous multifunctions. Taiwanese J. Math. 13 (2009), 2B, 757–775.
30Bui Trong Kien, Wong, M.-M.; Wong, N. C.; Yao, J. C., Degree theory for generalized variational inequalities and applications. European J. Oper. Res. 192 (2009), 730–736.
31Bui Trong Kien, Liou, Y. C.; Wong, N.-C.; Yao, J.-C., Subgradients of value functions in parametric dynamic programming. European J. Oper. Res. 193 (2009), 12–22.
32Bui Trong Kien, M. M. Wong, N. C. Wong, J. C. Yao, Solution existence of variational inequalities with pseudomonotone operators in the sense of Brézis. J. Optim. Theory Appl. 140 (2009),  249–263.
33Bui Trong Kien, Mu-Ming Wong, Ngai-Ching Wong, On the degree theory for general mappings of monotone type. J. Math. Anal. Appl. 340 (2008), 707–720.
34Bui Trong Kien, Ngai Ching Wong, Jen-Chih Yao, Generalized vector variational inequalities with star-pseudomonotone and discontinuous operators. Nonlinear Anal.: Theory, Methods & Applications 68 (2008), 2859–2871.
35Bui Trong Kien, N.C. Wong & J.C. Yao, On the solution existence of implicit quasivariational inequalities with discontinuous multifunctions. Optimization 57 (2008), 515–526.
36Bui Trong Kien, N.-C. Wong, and J.-C. Yao, Necessary conditions for multiobjective optimal control problems with free end-time. SIAM J. Control Optim. 47 (2008), 2251–2274.
37Bui Trong Kien, Jen-Chih Yao, Localization of generalized normal maps and stability of variational inequalities in reflexive Banach spaces. Set-Valued Anal. 16 (2008), 399–412.
38Bui Trong Kien, Lower semicontinuity of the solution map to a parametric generalized variational inequality in reflexive Banach spaces. Set-Valued Anal. 16 (2008), 1089–1105.
39Lu-Chuan Ceng, Bui Trong Kien, N. C. Wong, Convergence analysis of a hybrid relaxed-extragradient method for monotone variational inequalities and fixed point problems. Taiwanese J. Math. 12 (2008), 2549–2568.
40Bui Trong Kien, J.-C. Yao, Nguyen Dong Yen, On the solution existence of pseudomonotone variational inequalities, J. Glob Optim., 41 (2008), 135-145.
41Nguyen Dong Yen, J.-C. Yao, Bui Trong Kien, Covering properties at positive-order rates of multifunctions and some related topics, J. Math. Anal. Appl., 338 (2008), 467-478.
42Bui Trong Kien, M. -M. Wong, On the solution stability of variational inequalities. J. Global Optim. 39 (2007),  101–111.
43Bui Trong Kien, N. C. Wong, J. C. Yao, On the solution existence of generalized quasivariational inequalities with discontinuous multifunctions. J. Optim. Theory Appl. 135 (2007), 515–530.
44Bui Trong Kien, On the lower semicontinuity of optimal solution sets. Optimization 54 (2005), 123–130.
45Bui Trong Kien, Solution Sensitivity of Generalized Variational Inequalities and Continuity of Metric Projections, Ph.D. Thesis, Institute of Mathematics, Hanoi, Vietnam, 2003.
46Bui Trong Kien, Hölder continuity of solutions to a parametric problem of the calculus of variations. Nonlinear Anal. Forum 8 (2003), 123–136.
47Bui Trong Kien, The normalized duality mapping and two related characteristic properties of a uniformly convex Banach space. Acta Math. Vietnam. 27 (2002), 53–67.
48Bui Trong Kien, On the metric projection onto a family of closed convex sets in a uniformly convex Banach space. Nonlinear Anal. Forum 7 (2002), 93–102
49Bui Trong Kien, Solution sensitivity of a generalized variational inequality. Vietnam J. Math. 29 (2001), 97–113.
Preprints
1IMH20170503, Bui Trong Kien, N.H. Son, Existence of global strong solutions to the Navier-Stokes equations with large input data
2IMH20160601, Bui Trong Kien, J. C. Yao, Semicontinuity of the solution map to a parametric optimal control problem