Prof. Dr. Sc. Nguyễn Định

EDUCATION

• HDR (Habilitation a Diriger des Researches): University of Limoges, France, 2010
• PhD: Hanoi Institute of Mathematics, 1994
• M.Sc (Dynamical systems): Mathematical Research Institute, University of Utrecht, The Netherlands, June 1993.
• M.Sc (Mathematics): HanoiUniversity of Pedagogy I, 1985.
• Bachelor: Department of Mathematics, College of Education, HueUniversity, 1980. 
• Senior Lecturer: 1995
• Associate Professor: 2002
• Professor: 2019

RESEARCH INTERESTS

• Methods for solving  optimal control problems with phases restrictions
• Existence  for variational and optimal control problems in the absence of convexity
• Farkas lemmas for convex and non-convex systems and applications
• Theory of general optimization problems: optimality, duality, stability and well-posedness (convex, non-convex, nonsmooth problems)

TEACHING

• Calculus I, II; Engineering Mathematics; Mathematics for Bio-technology
• Operations research
• Theory of measure and integration; Functional analysis
• Elements of convex analysis and theory extremal  problems
• Optimization 2
• Decision making

PUBLICATIONS

• N. Dinh and H.X. Phu, Solving a class of regular optimal control problems with state constraints by the Method of Orienting Curves, Optimization, 25, 1992, pp. 231 — 247.
• N. Dinh and H.X. Phu, Solving a class of optimal control problems which are linear in the control variable by the Method of Orienting Curves, Acta Mathematica Vietnamica, 17, 1992, pp. 115 — 134.
• N. Dinh and H.X. Phu, Method of Orienting Curves and its application to an optimal control problem of a hydroelectric power plant. VN Journal of Mathematics, 20, 1992, pp. 40 — 53.
• N. Dinh, Solving a class of linear optimal control problems with several control variables by the Method of Orienting Curves. Optimization, 30, 1994, pp. 269 – 271.
• H.X. Phu and N. Dinh, Some remarks on the Method of Orienting Curves. Numerical Functional Analysis and Optimization, 16 (5& 6), 1995, pp. 755 – 763.
• E.J. Balder and N. Dinh, Some extensions of Berliocchi – Lasry theorem and extremum principles for classes of mathematical programming problems, VN Journal of Mathematics, 27 (1), 1999, pp. 23 – 31.
• N. Dinh and L.A. Tuan, Directional Kuhn-Tucker conditions and duality for quasidifferentiable programs, Acta Mathematica Vietnamica, 28(1), 2003, 17 – 38.
• V. Jeyakumar, G.M. Lee, and N. Dinh, New sequential Lagrange multiplier conditions characterizing optimality without constraint qualification for convex programs, SIAM Journal on Optimization, 14(2),2003, 534 – 547.
• V. Jeyakumar, G.M. Lee, and N. Dinh, Lagrange multiplier conditions characterizing optimal solution sets of convex programs, Journal of Optimization Theory and Application, 123(1), 2004, 83 – 103.
• N. Dinh, V. Jeyakumar, and G.M. Lee, Sequential Lagrangian duality for abstract convex programs without regularity condition, Journal of Optimization Theory and Application, 123, No. 1, 2005, 85-112.
• N. Dinh, G. M. Lee, and L. A. Tuan, Generalized Lagrange multipliers for non-convex directionally differentiable programs. In Continuous Optimization: current trends and modern applications, Edts. V. Jeyakumar and B. M. Glover, Springer, (September) 2005.
• N. Dinh, M.A. Goberna, and M.A. Lopez, From linear to convex systems: Consistency, Farkas’ lemma and applications, Journal of Convex Analysis, 13, No. 1, 2006, 133-133.
• V. Jeyakumar, Z.Y. Wu, G.M. Lee, and N. Dinh, Liberating the subgradient optimality conditions from constraint qualifications, Journal of Global Optimization, 36, 2006, 127-137.
• M.A. Goberna, V. Jeyakumar, and N. Dinh, Dual Characterizations of set containments with strict convex inequalities, Journal of Global Optimization, 34, 2006, 33 – 54.
• V. Jeyakumar, G.M. Lee, and N. Dinh, Characterization of solution sets of convex vector minimization problems, European Journal of Operational Research, 174, 2006, 1380 – 1395.
• N. Dinh, V. Jeyakumar, and G.M. Lee, Lagrange multiplier characterizations of solution sets of constrained pseudo-linear optimization problems, Optimization, No. 3, 55, 2006, 241 – 250.
• N. Dinh, M.A. Goberna, M.A. Lopez, and T.Q. Son, New Farkas type constraint qualifications in convex infinite programming, ESAIM Control, Optimisation and calculus of Variations, Vol. 13, No. 3, 2007, 580-597.
• N. Dinh, G. Vallet, and T.T.A. Nghia, Farkas-type results and duality for DC programs with convex constraints, Journal of Convex Analysis, Vol. 15, No. 2, 2008, 235 – 262.
• N. Dinh, On qualification conditions and Farkas’ lemma: Generalization and applications. Proceeding of the Sixth Vietnam-Korea Joint Workshop, Feb. 25-29, 2008, pp. 1- 22 (Editors: V.N. Phat and D.S. Kim), Publishing House for Sciences and Technology, Hanoi, 2008.
• T.Q. Son, N. Dinh, Characterizations of solution sets of convex infinite problems, TOP, 16, 2008, 147 – 163.
• N. Dinh, B. Mordukhovich, and T.T.A. Nghia, Qualification and optimality conditions for DC programs with infinite constraints. Acta Mathematica Vietnamica, 34(1), 2009, 123 – 153.
• N. Dinh, B. Mordukhovich, and T.T.A. Nghia, Subdifferentials of value functions and optimality conditions for some classes of DC and bilevel infinite and semi-infinite programs. Mathematical Programming, Vol. 123, Issue 1 (2010), 101-138.
• N. Dinh, J.-J. Strodiot, V.H., Nguyen, Duality and Optimality Conditions for Generalized Equilibrium Problems Involving DC Functions. Journal of Global Optimization, Vol. 48, 2010, 183-208.
• N. Dinh, T.T.A. Nghia, and G. Vallet, A closedness condition and its applications to DC programs with convex constraints. Optimization, Vol. 59, No. 4, 2010, 541-560
• S.Dempe, N. Dinh, J. Dutta, Optimality conditions for a simple convex bilevel programming problem. In: Variational Analysis and generalized Differentiation in Optimization and Control. R.S. Burachik, J-C Yao (eds.). Springer, Berlin, 2010.
• N. Dinh, M.A. Goberna, and M.A. Lopez, On the stability of the feasible set in mathematical programming. SIAM J. Optim., Vol. 20, No. 5, 2010, 2254-2280.
• N. Dinh, M.A. Lopez, M. Volle, Functional inequalities in the absence of convexity and lower semicontinuity with applications to optimization. SIAM J. Optim., Vol. 20, No. 5, 2010, 2540-2559.
• N. Dinh, M.A. Goberna, M.A. Lopez, M. Volle, Convex inequalities without constraint qualification nor closedness conditions and thẻi application in optimization. Set-valued and variational Analysis, Vol. 18, 2010, 423-445.
• G.M. Lee, G.S. Kim, N. Dinh, Optimality conditions for approximate solutions of convex semi-Infinite vector optimization problems optimality conditions for approximate solutions. In “Recent developments in vector optimization”. Eds.: Q.H. Ansari, J.-C Yao, Springer, 2012, pp. 275-295.
• N. Dinh, M.A. Goberna, M.A. Lopez, On the stability of the optimal value and the optimal set in optimization problems.Journal of Convex Analysis, Vol. 19 (4) (2012), 927-953.
• N. Dinh, T.H. Mo, Qualification conditions and Farkas-type results for systems involving composite functions, Vietnam Journal of Mathematics, Vol. 40 (4), 2012, 407 – 437.
• N. Dinh, Vallet G, and Volle M (2014) Functional inequalities and theorems of the alternative involving composite functions with applications. J. Global Optimization, 59 (2014) 837-863
• N. Dinh, E. Ernst, M.A. Lopez, M. Volle (2014) An approximate Hahn-Banach theorem for positively homogeneous functions. Optimization (to appear) DOI: 10.1080/02331934.2013.864290 http://www.tandfonline.com/doi/abs/10.1080/02331934.2013.864290#.UrZnSyd6SSo
• N. Dinh, M.A. Goberna, M.A. Lopez, T.H. Mo (2014) From Farkas to Hahn-Banach theorem. SIAM J. Optim.,24 (2014) 678-701.
• Dinh, V. Jeyalumar (2014), Farkas’ Lemma: Three Decades of Generalizations for Mathematical Optimization. Top 22 (2014) 1-22.
• Dinh, V. Jeyalumar (2014), Rejoinder on Farkas’ Lemma: Three Decades of Generalizations for Mathematical Optimization. Top 22 (2014) 41-44.
• N. Dinh, E. Ernst, M.A. Lopez, M. Volle, An approximate Hahn-Banach theorem for positively homogeneous functions. Optimization. 64 (2015), no. 5, 1321–1328.
• N. Dinh, T.H. Mo, Generalizations of the Hahn-Banach theorem revisited, Taiwanese Journal of Mathematics, 19 (2015), no. 4, 1285-1304, DOI: 10.11650/tjm.19.2015.5046.
• N. Dinh, T.H. Mo, Farkas lemma for convex systems revisited and applications to sublinear-convex optimization problems. Vietnam J. Math. 43 (2015), no. 2, 297-321.
• N. Dinh, M.A. Goberna, M.A. Lopez, T.H. Mo, Farkas-type results for vector-valued functions with applications. Journal of Optimization Theory and Applications, 173 (2017), 357-390
• N. Dinh, M.A. Goberna, D.H. Long, M.A. Lopez, New Farkas-type results for vector-valued functions: The non-abstract approach. Journal of Optimization Theory and Applications, 182 (2019), 4 – 29.
• N. Dinh, M.A. Goberna, M.A. Lopez, M. Volle, A unifying approach to robust convex infinite optimization duality. Journal of Optimization Theory and Applications, 174 (2017), 650 – 685.
• N. Dinh, D.H. Long, Complete characterizations of robust strong duality for robust vector optimization problems. Vietnam Journal of Mathematics (to appear, 2018).
• N. Dinh, M.A. Goberna, D.H. Long, M.A. Lopez, New Farkas-type results for vector-valued functions: The non-abstract approach. Journal of Optimization Theory and Applications, 182 (2019), 4 – 29.
• M. J. Canovas, N. Dinh, D.H. Long, J. Parra, A Farkas lemma approach to calmness of linear inequality systems. Optimization Letters, 13, 2019, 295-307.
• N. Dinh, M.A. Goberna, M.A. Lopez, T.H. Mo, Robust optimization revisited via robust vector Farkas lemmas. Optimization, 66 (No.6) (2017), 939-963
• N. Dinh, T.H. Mo, G. Vallet, M. Volle, A unified approach to robust Farkas-type results with applications to robust optimization problems. SIAM J. Optimization, 27 (2017), 1075-110
• N. Dinh, M.A. Goberna, M.A. Lopez, M. Volle, Characterizations of robust and stable duality for linearly perturbed uncertain optimization problems. In: R. Burachik, G.Y. Li (Edts.) From analysis to visualization: A celebration of the life and legacy of Jonathan M. Borwein, Callagan, Springer, Australia, 2017.
• N. Dinh, M.A. Goberna, M.A. Lopez, M. Volle, Convexity and closedness in stable robust duality. Optimization Letters, 13, 2019, 325-339.
• N. Dinh, M.A. Goberna, M. Volle, Duality for the Robust sum of functions. Set-Valued and Variational Analysis (2019, OnlineFirst)
• N. Dinh, D.H. Long, Sectional Convexity of Epigraphs of Conjugate Mappings with Applications to Robust Vector Duality. Acta Mathematica Vietnamica (to appear, 2019).
• N. Dinh, M.A. Goberna, M. Volle, Primal-dual optimization condition for the robust sum of function with applications. Applied Mathematics and Optimization, 80 (2019) 643–664
• Nguyen Dinh, D.H. Long , J.-C. Yao: Duality for Robust Linear Infinite Programming Problems Revisited. Vietnam Journal of Mathematics: 48 (2020), no. 3, 589–613
• N. Dinh, D.H. Long , T.H. Mo , J.-C. Yao: Approximate Farkas lemmas for vector systems with applications to convex vector optimization problems. Journal of Nonlinear and Convex Analysis, Vol. 21, (2020), p. 1225-1246
• J. Canovas, Nguyen Dinh, D.H. Long , J. Parra: A new approach to strong duality for composite vector optimization problems. Optimization, 70(8), 2021, p. 1637-1672
• Dinh, M.A. Goberna, M. Volle: Erratum to: Primal-dual optimization conditions for the robust sum of functions with applications. Applied Mathematics and Optimization. 84 (2021), pages 49–50N. Dinh,
• M.A. Goberna, D.H. Long , M. Volle: Duality for constrained robust sum optimization problems. Mathematical Programming, 189, pages271–297 (2021)S. Dempe , N. Dinh, J. Dutta , T. Pendit: Simple bilevel programming and extensions. Mathematical Programming: 188, 2021, p. 227-253
  https://doi.org/10.1007/s10107-020-01509-xDOI: 10.1080/02331934.2021.2017431.Dinh, D.H. Long: New Representations of Epigraphs of Conjugate Mappings and Lagrange, Fenchel-Lagrange Duality for Vector Optimization Problems. Optimization (online first).DOI: 10.1080/02331934.2022.2031192Dinh, M.A. Goberna, M.A. Lopez, M. Volle: Relaxed Lagrangian duality in convex infnite optimization: reducibility and strong duality. Optimization (online first).
• N. Dinh, M.A. Goberna, M.A. Lopez, M. Volle: Relaxed Lagrangian duality in convex infinite optimization: Reverse strong duality and optimality. Journal of applied and numerical optimization, 4, 2022, 3-18.DOI: 10.1007/s10957-022-02052-9.
• Dinh and D.H. Long, A Perturbation Approach to Vector Optimization Problems: Lagrange and Fenchel–Lagrange Duality. Journal of Optimization Theory and Applications,2022, (online first).https://doi.org/10.1007/s11228-022-00646-z
• Dinh, D.H. Long, M. Volle, Convex robust sum optimization problems with conic and set constraints: Duality and optimality conditions revisited. Set-valued and Variational Analysis, 2022, (Online first)Internal reports/preprints – University’s Bulletins
• N. Dinh, Relaxation by way of Young measures for a class of nonconvex variational problems, Bulletin of Science and Education, Hue University of Education, 9/1996, pp. 53 – 58.
• N. Dinh, Relaxation and the existence of relaxed and chattering solutions for a class of optimal control problems without convexity assumptions. Bulletin of Science and Education, Hue University of Education, 3/1997, pp. 29 – 36.
• N. Dinh and L.A. Tuan, Necessary and sufficient optimality conditions for locally Lipschitz programs with equality constraints, The Hue University Journal of Research, No. 4, 2000, pp. 11- 17 (in Vietnamese).
• N. Dinh and N.M. Nam, On weak stability by perturbations of an optimization problem, The Hue University Journal of Research, No. 10, 2002, pp. 21-28 (in Vietnamese).
• V. Jeyakumar and N. Dinh, Avoiding duality gaps in convex semi-definite programming without Slater’s condition, Applied Mathematics Research Report AMR04/6, 2004, School of Mathematics, University of New South Wales, Sydney, Australia (unpublished paper).
• V. Jeyakumar, N. Dinh, and G.M. Lee, A new closed cone constraint qualification for convex optimization. Applied Mathematics Research Report AMR04/8, 2004, School of Mathematics, University of New South Wales, Sydney, Australia (unpublished paper).
• N. Dinh, On results of Farkas type and its applications to convex optimization problems, Bulletin of Sciences, Ho Chi Minh City University of Pedagogy, 6, No. 40, 2005, 3 – 25 (in Vietnamese).
• N. Dinh and T.T.A, Nghia, Farkas lemma for systems involving convex and DC-functions, Bulletin of Sciences, Ho Chi Minh City University of Pedagogy, 6, No. 40, 2005, 41 – 52 (in Vietnamese).
• V. Jeyakumar, W. Song, N. Dinh, and G.M. Lee, Stable strong duality in convex optimization, Applied Mathematics Research Report AMR05/22, 2005, School of Mathematics, University of New South Wales, Sydney, Australia (unpublished paper).
• N. Dinh and T.Q. Son, Approximate optimality conditions and duality for convex infinite programming problems. Journal of Science and Technology Development, Vietnam National University-Ho Chi Minh city, 2008.
• N. Dinh and T. H. Mo, Farkas-type results for nonconvex systems involving composite functions with applications, Scientific Journal (Dalat University), 3A (6/ 2012), 32-40.
  Textbooks and lecture notes
• Nguyen Trong Chien, Phan van Danh, Nguyen Dinh, Nguyen Hoang, and Hoang Tron, Activities in teaching mathematics in high school – Analysis (in Vietnamese, document for teachers in high school to update mathematical knowledge, period 1997 – 2000), Hue University of Pedagogy, 1999.
• Phan Van Danh, Nguyen Dinh, Le Van Hap, Nguyen Hoang, Problems in Higher mathematics: Analysis of functions of one variable (in Vietnamese). Publishing House of Education, Hanoi, 2003.
• N. Dinh and N. Hoang, Real Analysis (topology and theory of measures and integration) (in Vietnamese). Publishing House of Education, Hanoi, 1999.
• N. Dinh and N. N. Hai, Theorems and Problems in Real Analysis (in Vietnamese). Publishing House of Education, Hanoi, 1999.
• Phan Van Danh, Nguyen Dinh, Le Van Hap, Nguyen Hoang, and Le V. Ngu, Higher Mathematics II: Analysis of functions of one variable (in Vietnamese). Publishing House of Education, Hanoi, 1998.
• N. Dinh, Modern Analysis I (in Vietnamese, Lecture for Master students), Hue University of Pedagogy, 1997.
  Conference reports (selected)
• N. Dinh (invited lecture), Generalized Lagrange multipliers for non-convex optimization. The First Korea-Japan Joint Symposium on Nonlinear Functional Analysis and Convex Analysis, Kyongju, Korea, August 2-5, 2002.
• N. Dinh, Generalized conditions and duality for nonconvex optimization problems. Conference on Operator Theory, Functional Analysis, and Finite Element Method, Bangkok, August 28, 2003.
• N. Dinh, Sequential Lagrange multiplier conditions characterizing optimality without constraint qualification for convex programs. Workshop on Optimization and Scientific Computing, Hanoi-Quangninh July 14-18, 2003.
• N. Dinh (invited lecture) On results of Farkas type and applications. The 4th Vietnam-Korea Workshop on Mathematical Optimization Theory and Applications, HoChiMinh city, February 18-20, 2004.
• N. Dinh, From linear to convex systems: Consistency, Farkas lemma and applications. Workshop on Optimization and Scientific Computing, Hanoi, April 20-24, 2005.
• N. Dinh (invited lecture), Farkas-type results and constraint qualifications in convex infinite programming. The Fifth Korea-Vietnam Joint Seminar on Mathematical Optimization Theory and Applications, Busan, February 8-11, 2006.
• N. Dinh, Approximate subdifferentials for a class of convex functions and applications. Workshop on Optimization and Scientific Computing, Bavi-Hatay, April 26-29, 2006.
• N. Dinh, A result on the stability of a class of parametric convex optimization problems, Workshop on Optimization and Scientific Computing, Bavi-Hatay, May 16-19, 2007.
• N. Dinh (invited lecture), On Farkas-Minkovski constraint qualification and Farkas lemma: Generalization and applications, The 6th CUD Spring School on Optimization and Applied mathematics, Ho Chi Minh city, March 4-10, 2007.
• N. Dinh (invited lecture), Duality for generalized equilibrium problems involving DC functions, International Symposium on Nonlinear Analysis and Optimization, Pukyong National University, Pusan, Korea, Feb. 16-18, 2008.
• N. Dinh (invited lecture), Closedness conditions and Farkas-type results: Generalizations and applications to convex and DC optimization problems, The sixth Korea-Vietnam Joint Seminar on Mathematical Optimization Theory and Applications, Nhatrang, Vietnam, February, 2008.
• N. Dinh (invited lecture) Qualification conditions and the stability of convex optimization problems. Workshop on Optimization and Scientific Computing, Bavi, Hanoi, April 22-25, 2009.
• N. Dinh, Qualification, optimality conditions and subdifferentials of optimal value functions for DC infinite and semi-infinite programs. European Conference on Operations Research 23rd (EURO XXIII), Bonn, July 5-9, 2009.
• N. Dinh, Optimality conditions for a simple class of bilevel optimization problem. Workshop on Optimization and Scientific Computing, Bavi-Hatay, April 20-23, 2010.
• N. Dinh (invited lecture), Convex inequalities without constraint qualification nor closedness condition and their applications in optimization. The 8th International Spring School/Workshop on Optimization and Its Applications, March 1-3, 2010, Nhatrang, Vietnam.
• N. Dinh, Stability of optimal values and optimal sets in optimization problems. Workshop on Optimization and Scientific Computing, Bavi-Hatay, Hanoi, April 20-24, 2011.
• N. Dinh (invited talk), Some new Farkas-type results and their applications to optimization. International Conference in Mathematics and Applications, UEL, VNU-HCMC, Dec. 2011.
• N. Dinh, Farkas lemma and Hahn-Banach theorem: Extensions and relations. Workshop on Optimization and Scientific Computing, Bavi-Hatay, Hanoi, April 18-21, 2012.
• N. Dinh, Some extensions of Farkas lemma and Hahn-Banach theorem. VMS-SMF Joint Congress, Hue, August 20-24, 2012.
• N. Dinh (joint with S. Dempe, J. Dutta), Optimality conditions for a simple MPEC problem. Workshop on Optimization and Scientific Computing, Bavi-Hatay, Hanoi, April 24-27, 2013.

OTHER INFORMATION

• Senior lecturer, Department of Mathematics, University of Pedagogy, Hue University, Hue city, Vietnam (September 1980 – June 2001)
• Associate Professor, Department of Mathematics-Informatics, Ho Chi Minh City University of Pedagogy (June 2001 – June 2005
• Head of Department of International Relations, Ho Chi Minh City University of Pedagogy (June 2005 – February 2006)
• Department of Mathematics, International University, Vietnam National University-Ho Chi Minh city (March 2006 – present). Head of Dept. of  Math.  from 2013 to 2017
• Projects
• Extended scalar/vector Farkas-type results with applications to optimization. Project type B from
• Vietnam National University – HoChiMinh city, code: B2019-28-02, 2019-2020.
• Some topics on systems with uncertainty and robust optimization. NAFOSTED, 101.01-2018.310, 2019-2020.
• Some extensions of Farkas lemmas with applications to optimization. NAFOSTED, 101.01-2015.27, 2016-2018
• A new approach to some classes of optmization problems. Vietnam National University-HCM city, 2015- 2017.
• Head of the project: “Some Farkas-type results and nonlinear optimization”, NAFOSTED Vietnam, 2012 – 2013.
• Head of the project “Characterizations of convex/nonconvex inequalities with applications to optimization theory”, Vietnam National University-HCM city, 2011- 2012.
• Head of the project “On DC and bilevel optimization problems”, Vietnam National University-HCM city, 2010.
• Head of the project “Qualitative study of some classes of single and multi-objective optimization problems with infinitely many constraints”, Vietnam National University-HCM city, 2009.
• Head of the project “On the study of some classes of optimization problems with DC functions and applications”, Ministry of Education and Training, 2008.
• Head of the project “Dual constraint qualifications and its applications to optimization theory” , Ministry of Education and Training, 2007.
• Head of the project “Farkas-type results for nonconvex systems ans its applications to optimization theory”, International University, Vietnam National University-Ho Chi Minh city, 2006.
• Head of the project CS.2005.23.77: “Extended version of Farkas lemma for systems involving reverse-convex constraints and applications” (2005-2006), Ho Chi Minh city University of Pedagogy, Vietnam.
• Co-Head of the National Basic Research Project 1.1.10/98: “Optimal algorithms and applications” (1998-2000) (with Dr. H.T. Phung, Hue University).
• Member of some projectsRough Analysis and Scientific Computing (National Foundation for Sciences &
• Technology Development, NAFOSTED, Vietnam, 2010-2011; Head: Prof. Dr.Sc. Hoang Xuan Phu),
  Rough analysis and its applications (National Basic Research Project, Hanoi Institute of Mathematics, 2006-2007, 2008-2009; Head: Prof. Dr.Sc. Hoang Xuan Phu),
• Existence of optimal solutions for some classes of problems in nonlinear analysis (B2005.23.68; Ministry of Sciences, Technology, and Environment, 2005-2006, Head: Assoc. Prof. Le Hoan Hoa, HCM City Univ. of Pedagogy),
• Rough analysis and its applications (National Basic Research Project, Hanoi Institute of Mathematics, 2003-2005 (National Basic Research Project, Hanoi Institute of Mathematics, Head: Prof. Dr.Sc. Hoang Xuan Phu),
• Analysis of non-smooth maps and its application to optimal control theory and optimization (National
• Basic Research Project, Hanoi Institute of Mathematics, 1998-2002, Head: Prof. Dr.Sc. Pham Huu Sach),
  Theory of dynamical systems (National Basic Research Project, National Center of Science and Technology of Vietnam, 1993-1995, Head: Prof. Dr.Sc. Nguyen Khoa Son),
• Methods of analysis of set-valued maps in non-smooth optimization and in dynamical system (National Basic Research Project, Hanoi Institute of Mathematics, 1992-1995).
  Conferences
• Member of Organizing Committee of International Conference in Mathematics and Applications, ICMA 2011, VNU-HCMC, December, 2011.
• Member of Organizing Committee of Workshop on Optimization and Scientific Computing, Hanoi Institute of Mathematics, Ba vi (Vietnam), April 2009; April, 2010; April 2011, April 2012, April 2013.
• Member of Scientific Committee of the 8th International School/Workshop on Optimization and Its Applications, Nhatrang (Vietnam), March 1-3, 2010.
• Member of Organizing Committee of Workshop on Optimization and Scientific Computing, Hanoi Institute of Mathematics, Ba vi (Vietnam), April, 2008.
• Member of Scientific Committee of The 6th CUD Spring School on Optimization and Applied Mathematics, Hanoi, July, 2008.
• Member of Organizing Committee of Workshop on Optimization and Scientific Computing, Hanoi Institute of Mathematics, Ba vi (Vietnam), April, 2007.
• Member of Scientific Committee of The 6th CUD Spring School on Optimization and Applied Mathematics, Ho Chi Minh city, March 4-10, 2007.
• Member of Organizing Committee of Workshop on Optimization and Scientific Computing, Hanoi Institute of Mathematics, Ba vi (Vietnam), April 26 – 29, 2006.
• Member of Organizing Committee of Workshop on Optimization and Scientific Computing, Hanoi Institute of Mathematics, Hanoi, May 18 – 22, 2005.
• Member of Organizing Committee of Workshop on Optimization and Scientific Computing, Hanoi Institute of Mathematics, Hanoi, May 5 – 9, 2004.
• Member of Scientific Committee of The 4 Vietnam-Korea Workshop on Mathematical Optimization Theory and Applications, Ho Chi Minh city, February 18 – 20, 2004.
  Participating and giving report/invited lectures
• The First Korea-Japan Joint Symposium on Nonlinear Functional Analysis and Convex Analysis, Kyongju, Korea August 2-5, 2002
• Conference on Operator Theory, Functional Analysis, and Finite Element Method, Bangkok, Auguat 28, 2003.
• The Fifth Korea-Vietnam Joint Seminar on Mathematical Optimization Theory and Applications, Busan, Korea, February 8-11, 2006.
• International Symposium on Nonlinear Analysis and Optimization, Pukyong National University, Pusan, Korea, Feb. 16-18, 2008.
• The sixth Korea-Vietnam Joint Seminar on Mathematical Optimization Theory and Applications, Nhatrang, Vietnam, February, 2008.
• European Conference on Operations Research 23rd (EURO XXIII), Bonn, July 5-9, 2009.
  International Conference in Mathematics and Applications, UEL, VNU-HCMC, Dec. 2011.
• VMS-SMF (Vietnam-France) Joint Congress, Hue (VN), August 20-24, 2012.
  Scientific visits
• Institute of Mathematics, University of Utrecht, The Netherlands: June to November 1993.
• Institute of Mathematics, University of Utrecht,The Netherlands: November 1994 to February 1995.
• Jean Monet University, Saint-Etienne, France: January to May 1999.
• Hanoi Institute of Mathematics: October to December 2000 (a grand for short term advanced research).
• Pukyong National University, Pusan, Korea: February 2002 to February 2003 (Postdoctoral Fellowship from the Korea Science and Engineering Foundation).
• Mahidol University, Bangkok, Thailand: August 2003.
• School of Mathematics, University of New South Wales, Sydney, Australia: October to November 2003.
• Laboratory of Applied Mathematics, University of PAU, France: May -June, 2004.
• Center for Inter-discipline Scientific Computing, University of Heidelberg, Germany: August to September, 2004.
• Dept. of Operations Research and Statistics, University of Alicante, Spain: Oct., 2004.
• Department of Operation Research and Statistics, University of Alicante, Spain: December, 2005.
• Department of Applied Mathematics, Faculty of Sciences, Pukyong National University, Pusan, Korea: February, 2005.
• Laboratory of Applied Mathematics, University of PAU, France: September, 2006
• Dept. of Operation Research and Statistics, University of Alicante, Spain: June, 2007.
• Department of Mathematics, Faculty of Sciences, University of Namur, Belgium, July-August, 2007.
• Department of Mathematics, Faculty of Sciences, Pukyong National University, Pusan, Korea: February 3- Feb.18, 2008.
• Department of Applied Mathematics, Faculty of Laboratory of Applied Mathematics, University of PAU, France: June, 2008.
• Dept. of Operation Research and Statistics, University of Alicante, Spain: July, 2008.
• Dept. of Mathematics, Faculty of Science, University of Namur, Belgium, August, 2008.
• Dept. of Operation Research and Statistics, University of Alicante, Spain: July, 2009.
• Department of Applied Mathematics, University of Metz, France, August, 2009.
• Centre de Recerca Matematica, Universitat Autonoma de Barcelona (UAB), Spain, September, 2010.
• Dept. Math., University of Limoges, September, 2010.
• Dept. of Operation Research and Statistics, University of Alicante, Spain: October, 2012. Dept. of Operation Research and Statistics,
• University of Alicante, Spain: September 2015; June-July 2016; February, 2018.
• Center for General Education, China Medical University, Taiwan, July-August, 2019.