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 114
Tel: +84 (0)4 37563474/ 114
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
1Bui 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.
2Bui 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.
3N. 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.
4N. 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.
5Bui 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.
6Bui 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.
7Bui 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.
8Bui Trong Kien, Nhu, V. H, Second-order necessary optimality conditions for a class of semilinear elliptic optimal control problems with mixed pointwise constraints. SIAM J. Control Optim. 52 (2014), 1166–1202.
9Bui 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.
10Bui 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.
11Bui 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 J. Control Optim., 50 (2012), 2889 -- 2906.
12Bui 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.
13Nguyen 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.
14Nguyen Thi Toan, Bui Trong Kien, Subgradients of the value function to a parametric optimal control problem. Set-Valued Var. Anal. 18 (2010), 183–203.
15Bui 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.
16Bui 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.
17Bui 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.
18Bui 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.
19Bui 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.
20Bui 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.
21Bui Trong Kien, N.C. Wong & J.C. Yao, On the solution existence of implicit quasivariational inequalities with discontinuous multifunctions. Optimization 57 (2008), 515–526.
22Bui 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.
23Bui 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.
24Bui 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.
25Lu-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.
26Bui Trong Kien, J.-C. Yao, Nguyen Dong Yen, On the solution existence of pseudomonotone variational inequalities, J. Glob Optim., 41 (2008), 135-145.
27Nguyen 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.
28Bui Trong Kien, M. -M. Wong, On the solution stability of variational inequalities. J. Global Optim. 39 (2007),  101–111.
29Bui 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.
30Bui Trong Kien, On the lower semicontinuity of optimal solution sets. Optimization 54 (2005), 123–130.
31Bui Trong Kien, Solution Sensitivity of Generalized Variational Inequalities and Continuity of Metric Projections, Ph.D. Thesis, Institute of Mathematics, Hanoi, Vietnam, 2003.
32Bui Trong Kien, Hölder continuity of solutions to a parametric problem of the calculus of variations. Nonlinear Anal. Forum 8 (2003), 123–136.
33Bui Trong Kien, The normalized duality mapping and two related characteristic properties of a uniformly convex Banach space. Acta Math. Vietnam. 27 (2002), 53–67.
34Bui 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
35Bui 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
3IMH2012/12/01, Bui Trong Kien, Nguyen Dong Yen, J. - C. Yao, Corrigendum on "Covering properties at positive-order rates of multifunctions and some related topics"