Nguyen Dong Yen


Full Professor, Doctor of Science

Department of Numerical Analysis and Scientific Computing
Research interests: Optimization Theory, Nonsmooth Analysis, Set-Valued Analysis, Variational Inequalities, Numerical Analysis and Scientific Computing


Address
Office: Building A5, Room 213
Tel: +84 (0)4 37563474 /213
Email: ndyen AT math.ac.vn

Education and academic degrees:

  • 1999: Dr. Sci., University of Lodz (Lodz, Poland)
  • 1988: Ph.D., Hanoi Institute of Mathematics (Hanoi, Vietnam)
  • 1981: B. s. , The Belorussian State University (Minsk, Belorus).


Research areas:

  • Optimization
  • Nonsmooth Analysis
  • Set-Valued Analysis
  • Variational Inequalities
  • Numerical Analysis and Scientific Computing


PUBLICATIONS

 

List of publications in MathSciNet


List of recent publications
1Vu Thi Huong, Jen-Chih Yao, Nguyen Dong Yen, On the Stability and Solution Sensitivity of a Consumer Problem, Journal of Optimization Theory and Applications, 175 (2017), 567--589.
2N. T. T. Huong, J.C. Yao, Nguyen Dong Yen, Connectedness structure of the solution sets of vector variational inequalities, Optimization, 66 (2017), 889-901.
3P. D. Khanh, J.-C. Yao, Nguyen Dong Yen, The Mordukhovich subdifferentials and directions of descent, Journal of Optimization Theory and Applications, 172 (2017),518--534.
4Bui Ngoc Muoi, Nguyen Dong Yen, Local stability and local convergence of the basic trust-region method, Journal of Optimization Theory and Applications, 72 (2017), 578-593
5Nguyen Thi Van Hang, Nguyen Dong Yen, On the Problem of Minimizing a Difference of Polyhedral Convex Functions Under Linear Constraints, Journal of Optimization Theory and Applications, 171 (2016), 617–642.
6Nguyen Dong Yen, An Introduction to Vector Variational Inequalities and Some New Results, Acta Mathematica Vietnamica, 41 (2016), 505–529.
7Nguyen Thi Thu Huong, Yao J.-C., Nguyen Dong Yen, Polynomial vector variational inequalities under polynomial constraints and applications. SIAM Journal on Optimization 26 (2016), 1060–1071.
8Nguyen Thi Vinh, Nguyen Dong Yen, D.S. Kim, N.N. Tam, Duality gap function in infinite dimensional linear programming. Journal of Mathematical Analysis and Applications, 437 (2016), 1–15.
9Nguyen Thai An, Nguyen Mau Nam , Nguyen Dong Yen, A D.C. Algorithm via Convex Analysis Approach for Solving a Location Problem Involving Sets, Journal of Convex Analysis 23 (2016), 77-101.
10Duong Thi Kim Huyen, Nguyen Dong Yen, Coderivatives and the solution map of a linear constraint system, SIAM Journal on Optimization 26(2016), 986–1007.
11Nguyen Thi Thu Huong, Nguyen Dong Yen, The Adaptive Parameter Control Method and Linear Vector Optimization, Vietnam Journal of Mathematics, 43(2015), 471 -486.
12Duong Thi Viet An, Nguyen Dong Yen, Differential stability of convex optimization problems under inclusion constraints. Applicable Analysis 94 (2015), 108 - 128.
13Nguyen Thi Van Hang, Nguyen Dong Yen, Optimality conditions and stability analysis via the Mordukhovich subdifferential, Numerical Functional Analysis and Optimization, 36 (2015), 364 - 386.
14Nguyen Thi Thu Huong, Nguyen Dong Yen, The Pascoletti-Serafini scalarization scheme and linear vector optimization. J. Optim. Theory Appl. 162 (2014), 559–576.
15Nguyen Thanh Qui, Nguyen Dong Yen, A class of linear generalized equations. SIAM J. Optim. 24 (2014), 210–231.
16G.M. Lee, Nguyen Dong Yen, Coderivatives of a Karush-Kuhn-Tucker point set map and applications, Nonlinear Analysis: Theory, Methods & Applications 95 (2014), 191–201.
17N. T. T. Huong, P. D. Khanh, Nguyen Dong Yen, Multivalued Tikhonov trajectories  of general affine variational inequalities, Journal of Optimization Theory and Applications, 158 (2013), 85 - 96.
18Hoang Ngoc Tuan, Nguyen Dong Yen, Convergence of Pham Dinh-Le Thi's algorithm for the trust-region subproblem,  Journal of Global Optimization, 55 (2013), 337 – 347.
19T. Pham Dinh, Shashi Kant Mishra, Nguyen Dong Yen, Preface [Special Issue: International Conference on Optimization and Its Applications (ICOIA-BHU-2010)]. Held at Banaras Hindu University, Varanasi, February 16–18, 2010. Optim. Lett. 6 (2012), 219–220.
20D. S. Kim, N. N. Tam, Nguyen Dong Yen, Solution existence and stability of quadratically constrained convex quadratic programs. Optim. Lett. 6 (2012), no. 2, 363–373.
21Nguyen Dong Yen, Linear fractional and Convex quadratic vector optimization problems, Springer, INBN: 978-3-642-21113-3, 297 -- 328.
22Nguyen Dong Yen, N. V. Tuyen, On the concept of generalized order optimality,  Nonlinear Analysis, 75 (2012), 1592 -- 1601.
23Le Thi Hoai An, Pham Dinh Tao, Nguyen Dong Yen, Behavior of DCA sequences for solving the trust-region subproblem,  Journal of Global Optimization, 53 (2012), 317 -- 329.
24G. M. Lee, N. N. Tam, Nguyen Dong Yen, Stability of linear-quadratic minimization over Euclidean balls,  SIAM Journal of Optimization, 22 (2012), 936 -- 952.
25N. T. T. Huong, T. N. Hoa, Ta Duy Phuong, Nguyen Dong Yen, A property of bicriteria affine vector variational inequalities, Applicable Analysis, 91 (2012), 867 – 1879.
26Nguyen Dong Yen, J.-C. Yao, Monotone affine vector variational inequalities, Optimization  60 (2011), 53 - 68.
27G. M. Lee, Nguyen Dong Yen, Fr\'echet and normal coderivatives of implicit multifunctions,  Applicable Analysis 90 (2011), 1011 - 1027.
28N. Q. Huy, Nguyen Dong Yen, Minimax variational inequalitiesActa Math. Vietnamica  36 (2011), 265 -- 281.
29N. H. Chieu, T. D. Chuong, J.-C. Yao, Nguyen Dong Yen, Characterizing convexity of a function by its Fr\ echet and limiting second-order subdifferentials,  Set-Valued and Variational Analysis  19 (2011), 75 - 96.
30L. T. H. An, P. D. Tao, Nguyen Dong Yen, Properties of two DC algorithms in quadratic programming, Journal of Global Optimization  49 (2011), 481 - 495.
31N. T. Qui, Nguyen Dong Yen, Some properties of polyhedral multifunctions,  Journal of Nonlinear and Convex Analysis, 12 (2011), 483 -- 499.
32J.-C. Yao, Nguyen Dong Yen, Parametric variational system with a smooth-boundary constraint set, In:  Variational Analysis and Generalized Differentiation in Optimization and Control  Eds.), Springer Verlag  47  (2010), 205 - 221.
33Thai Doan Chuong, J.-C. Yao, Nguyen Dong Yen, Further results on the lower semicontinuity of efficient point multifunctions,Pacific Journal of Optimization, 6 (2010), 405 -- 422.
34N. H. Chieu, J.-C. Yao, Nguyen Dong Yen, Relationships between Robinson robust stability and Lipschitz-like behavior of implicit multifunctions, Nonlinear Anal.: Theory, Methods & Appl., 72 (2010), 3594 -- 3601.
35X. Q. Yang, Nguyen Dong Yen, Structure and weak sharp minimum of the Pareto solution set for piecewise linear multiobjective optimization, J. Optim. Theory Appl., 147 (2010), 113 -- 124.
36 G. M. Lee, N. N. Tam, Nguyen Dong Yen, Stability of a class of quadratic programs with a conic constraint, Taiwanese J. Math., 13 (2009), 1823 -- 1836.
37Nguyen Dong Yen, J.-C. Yao, Point-based sufficient conditions for metric regularity of implicit multifunctions, Nonlinear Analysis: Theory, Methods & Applications, 70 (2009), 2806-2815.
38J.-C. Yao, Nguyen Dong Yen, Coderivative calculation related to a parametric affine variational inequality, Part 2: Applications, Pacific Journal of Optimization,  5 (2009), 493-506.
39J.-C. Yao, Nguyen Dong Yen, Coderivative calculation related to a parametric affine variational inequality, Part 1: Basic calculations,  Acta Math. Vietnamica,  34 (2009), 157-172.
40B. S. Mordukhovich, N. M. Nam, Nguyen Dong Yen, Subgradients of marginal functions in parametric mathematical programming,  Math. Program., 116 (2009), 369-396.
41Nguyen Dong Yen, Parametric optimization problems and parametric variational inequalities, Vietnam Journal of Mathematics, 37 (2009), 191-223.
42Bui Trong Kien, J.-C. Yao, Nguyen Dong Yen, On the solution existence of pseudomonotone variational inequalities, J. Glob Optim., 41 (2008), 135-145.
43N. N. Tam, J.-C. Yao, Nguyen Dong Yen, Solution methods for pseudomonotone variational inequalities, J. Optim Theory Appl.,  138 (2008), 253-273.
44G. M. Lee, N. N. Tam, Nguyen Dong Yen, Normal coderivative for multifunctions and implicit function theorems, J. Math. Anal. Appl., 338 (2008), 11-22.
45Nguyen 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.
46Nguyen Dong Yen, J. -C. Yao, Vertical tangent vectors to the graph of a multifunction, Taiwanese Journal of Mathematics, 12 (2008), 1293-1302.
47N. M. Nam, Nguyen Dong Yen, Relationships between approximate Jacobians and coderivatives, J. Nonlinear Convex Anal. 8 (2007), 121-133.
48Gue Myung Lee, Nguyen Nang Tam, Nguyen Dong Yen, Continuity of the solution map in parametric affine variational inequalities, Set-Valued Anal. 15 (2007), 105 - 123.
49Tran Ninh Hoa, Nguyen Quang Huy, Ta Duy Phuong, Nguyen Dong Yen, Unbounded components in the solution sets of strictly quasiconcave vector maximization problems, J. Global Optim. 37 (2007), 1 - 10.
50B. S. Mordukhovich, N. M. Nam, Nguyen Dong Yen, Frechet subdifferential calculus and optimality conditions in nondifferentiable programming, Optimization 55 (2006), 685 - 708.
51G. M. Lee, N. N. Tam, Nguyen Dong Yen, Continuity of the solution map in quadratic programs under linear perturbations, J. Optim. Theory Appl. 129 (2006), 415 - 423.
52G. M. Lee, N. N. Tam, Nguyen Dong Yen, Lower semicontinuity of the KKT point set in quadratic programs under linear perturbations, Vietnam J. Math. 34 (2006), 411 - 422.
53G. M. Lee, N. N. Tam, Nguyen Dong Yen, On the optimal value function of a linearly perturbed quadratic program, J. Global Optim. 32 (2005), N0 1, 119 - 134.
54Tran Ninh Hoa, Ta Duy Phuong, Nguyen Dong Yen, Linear fractional vector optimization problems with many components in the solution sets. J. Ind. Manag. Optim. 1 (2005), 477 - 486.
55T. N. Hoa, Ta Duy Phuong, Nguyen Dong Yen, Bicriteria strictly quasiconcave maximization on noncompact sets. Nonlinear Anal. Forum 10 (2005),  137 - 144.
56T. N. Hoa, Ta Duy Phuong, Nguyen Dong Yen, On the parametric affine variational inequality approach to linear fractional vector optimization problems,  Vietnam J. Math. 33 (2005), 477 - 489.
57Gue Myung Lee, Nguyen Nang Tam, Nguyen Dong Yen, Quadratic programming and affine variational inequalities: a qualitative study, Series ``Nonconvex Optimization and its Applications", Vol. 78, XIV + 345 p., Springer Verlag, 2005.
58Nguyen Quang Huy, Nguyen Dong Yen, Contractibility of the solution sets in strictly quasiconcave vector maximization on noncompact domains, J. Optim. Theory Appl. 124 (2005), 615 - 635.
59Nguyen Quang Huy, Nguyen Dong Yen, Remarks on a conjecture of J. Benoist. Nonlinear Anal. Forum 9 (2004), 109 - 117.
60V. Jeyakumar, Nguyen Dong Yen, Solution stability of nonsmooth continuous systems with applications to cone-constrained optimization. SIAM J. Optim. 14 (2004), 1106 - 1127.
61G. M. Lee, N. N. Tam, Nguyen Dong Yen, Some recent results on quadratic programs and affine variational inequality problems under linear perturbations, In: Fixed point theory and applications, Vol. 5, (Y. J. Cho, J. K. Kim and S. M. Kang, Eds.), Nova Sci. Publ., NY, 2004, 59 - 77.
62Nguyen Dong Yen, On a problem of B. Ricceri on variational inequalities, In: Fixed point theory and applications, Vol. 5 (Y. J. Cho, J. K. Kim and S. M. Kang, Eds.), Nova Sci. Publ., NY, 2004, 163 - 173.
63N. Q. Huy, Ta Duy Phuong, Nguyen Dong Yen, On the contractibility of the efficient and weakly efficient sets in R2. In: Equilibrium problems and variational models (Erice, 2000), 265 - 279, Nonconvex Optim. Appl. 68, Kluwer Acad. Publ., Norwell, MA, 2003.
64Nguyen Dong Yen, Hung, Nguyen Xuan, A criterion for the compactness of the solution set of a linear complementarity problem. In: Fixed point theory and applications, Vol. 2 (Y. J. Cho, J. K. Kim and S. M. Kang, Eds.), Nova Sci. Publ., NY, 2001, 135 - 141.
65Nguyen Dong Yen, Bui Trong Kim, Linear operators satisfying the assumptions of some generalized Lax-Milgram theorems, Acta Math. Vietnam. 26 (2001), N0 3, 407 - 417.
66G. M. Lee, Nguyen Dong Yen, A result on vector variational inequalities with polyhedral constraint sets. J. Optim. Theory Appl. 109 (2001), 193 - 197.
67Hoang Xuan Phu, Nguyen Dong Yen, On the stability of solutions to quadratic programming problems. Math. Program. 89 (2001),  Ser.A, 385 - 394.
68Nguyen Dong Yen, G. M. Lee, Some remarks on the elliptic regulization method, In: Fixed Point Theory and Applications (Y. J. Cho, Ed.), Nova Science Publishers, New York, 2000, 127 - 134.
69Nguyen Dong Yen, Gue Myung Lee, On monotone and strongly monotone vector variational inequalities. In: Vector Variational Inequalities and Vector Equilibria. Mathematical Theories (F. Giannessi, Ed.), Kluwer Academic Publishers, Dordrecht, 2000, 467 - 478.
70N. N. Tam, Nguyen Dong Yen, Stability of the Karush-Kuhn-Tucker point set in a general quadratic programming problem. Vietnam J. Math. 28 (2000), No 1, 67 - 79.
71Nguyen Dong Yen, Ta Duy Phuong, Connectedness and stability of the solution set in linear fractional vector optimization problems. In: "Vector Variational Inequalities and Vector Equilibria. Mathematical Theories", F. Giannessi, Ed., Nonconvex Optim. Appl. 38, Kluwer Academic Publishers, Dordrecht, 2000, 479 - 489.
72Nguyen Nang Tam, Nguyen Dong Yen, Continuity properties of the Karush-Kuhn-Tucker point set in quadratic programming problems. Math. Programming 85 (1999), 193 - 206.
73Lee Gue Myung, Kim Do Sang, Byung Soo, Nguyen Dong Yen, Lee, On a strongly monotone vector variational inequality. Nonlinear Anal. Forum 3 (1998), 151–176.
74Gue Myung Lee, Do Sang Kim, Byung Soo Lee, Nguyen Dong Yen, Vector variational inequality as a tool for studying vector optimization problems. Nonlinear Analysis: Theory, Methods & Applications 34 (1998), 745 - 765.
75Paolo Cubiotti, Nguyen Dong Yen, A result related to Ricceri's conjecture on generalized quasi-variational inequalities, Arch. Math. 69 (1997), 507 - 514.
76Nguyen Dong Yen, Gue Myung Lee, Solution sensitivity of a class of variational inequalities. J. Math. Anal. Appl. 215 (1997), 48 - 55.
77Nguyen Dong Yen, Stability of the solution set of perturbed nonsmooth inequality systems and application. J. Optim. Theory Appl. 93 (1997), 199 - 225.
78Pham Huu Sach, Nguyen Dong Yen, Convexity criteria for set-valued maps. Set-Valued Analysis 5 (1997), 37 - 45.
79W. Oettli, Nguyen Dong Yen, An example of a bad quasicomplementarity problem. J. Optim. Theory Appl. 90 (1996), 213 - 215.
80W. Oettli, Nguyen Dong Yen, Quasicomplementarity problems of R0 type. J. Optim. Theory Appl. 89 (1996), 467 - 474.
81Nguyen Dong Yen, Lipschitz continuity of solutions of variational inequalities with a parametric polyhedral constraint. Math. Oper. Research 20 (1995), 695 - 708.
82Oettli Werner, Nguyen Dong Yen, Continuity of the solution set of homogeneous equilibrium problems and linear complementarity problems, In: Variational Inequalities and Network Equilibrium Problems (F. Giannessi and A. Maugeri, Eds.), Plenum Press, New York, 1995, 225 - 234.
83Nguyen Dong Yen, A mean value theorem for semidifferentiable functions. Vietnam J. Math. 23 (1995), 221 - 228.
84Nguyen Dong Yen, On G-semidifferentiable functions in Euclidean spaces. J. Optim. Theory Appl. 85 (1995), 377 - 392.
85Nguyen Dong Yen, Holder continuity of solutions to a parametric variational inequality. Appl. Math. Optim. 31 (1995), 245 - 255.
86Nguyen Dong Yen, On an existence theorem for generalized quasi-variational inequalities. Set-Valued Anal. 3 (1995), 1 - 10.
87Ta Duy Phuong, Pham Huu Sach, Nguyen Dong Yen, Strict lower semicontinuity of the level sets and invexity of a locally Lipschitz function. J. Optim. Theory Appl. 87 (1995), 579 - 594.
88Nguyen Dong Yen, On a class of discontinuous vector-valued functions and the associated quasi-varia-tional inequalities. Optimization 30 (1994), 197 - 203.
89G. Mastroeni, M. Pappalardo, Nguyen Dong Yen, Image of a parametric optimization problem and continuity of the perturbation function. J. Optim. Theory Appl. 81 (1994), 193 - 202.
90Pham Huu Sach, Nguyen Dong Yen, B.D. Craven, Generalized invexity and duality theories with multifunctions. Numer. Funct. Anal. Optim. 15 (1994), 131 - 153.
91Nguyen Dong Yen, Pham Huu Sach, On locally Lipschitz vector-valued invex functions. Bull. Austral. Math. Soc. 47 (1993), 259 - 271.
92Pham Huy Dien, Nguyen Dong Yen, Correction: "On implicit function theorems for set-valued maps and their application to mathematical programming under inclusion constraints'' [Appl. Math. Optim. 24 (1991), 35–54]. Appl. Math. Optim. 26 (1992), 111
93B. D. Craven, Pham Huu Sach, Nguyen Dong Yen, Ta Duy Phuong, A new class of invex multi-functions. In: Nonsmooth Optimization: Methods and Applications (F. Gianessi, ed.), Gordon and Breach Science Publishers, 1992, 52 - 69
94Pham Hong Quang, Nguyen Dong Yen, New proof for a theorem of F. Giannessi. J. Optim. Theory Appl. 68 (1991), 385 - 387.
95Pham Huy Dien, Nguyen Dong Yen, On implicit function theorems for set-valued maps and their application to mathematical programming under inclusion constraints. Appl. Math. Optim. 24 (1991), 35 - 54.
96Nguyen Dong Yen, Pham Huy Dien, On differential estimations for marginal functions in mathematical programming problems with inclusion constraints. In: Lecture Notes in Control and Information Sciences, Springer Verlag, Berlin, 143 (1990), 244 - 251.
97Nguyen Dong Yen, Trinh Cong Dieu, On local controllability of nondifferentiable discrete-time systems with nonconvex constraints on controls. Optimization 20 (1989), 189 - 199.
98Nguyen Dong Yen, Implicit function theorems for set-valued maps. Acta Math. Vietnam. 12 (1987), 17 - 28.
99Nguyen Dong Yen, Local controllability for Lipschitzian discrete-time systems. Acta Math. Vietnam. 11 (1986), 172 - 179.
100Pham Huy Dien, Nguyen Dong Yen, A remark on the Clarke tangent cone. Acta Math. Vietnam. 10 (1985), 144 - 147.
Preprints
1IMH2012/12/01, Bui Trong Kien, Nguyen Dong Yen, J. - C. Yao, Corrigendum on "Covering properties at positive-order rates of multifunctions and some related topics"