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Assoc.Prof. Dr.
Department of Mathematical Analysis, Institute of Mathematics,
Office: Room 106, Building A5
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| Education
Ph.D., Institute of Mathematics,
Hanoi, 1980
Graduate, Hanoi State University,
1968
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| Permanent address
Department
of Mathematical Analysis,
Institute
of Mathematics, VAST
18 Hoang Quoc Viet Road, CauGiay District,
10307, Hanoi, Viet nam
email : dvluu@math.ac.vn
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| Fields of Interest
Optimization Theory and
Nonsmooth Analysis
Generalized convex functions
and applications
Stability in nonsmooth
optimization
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Selected publications
(with W. Oettli) Necessary
optimality conditions for nonsmooth minimax problems. Zeitschrift für
Analysis und ihre Anwendungen, 12(1993), No4, 709-721.
(with B. D. Craven) Constrained
minimax for a vector-valued function. Optimization, 31(1994), 199-208.
(with W. Oettli) Higher-order
optimality conditions for a minimax. Bull. Austral. Math. Soc., 54(1996),
509-516.
(with B. D. Craven and B. M.
Glover) Strengthened invex and perturbation. Math. Meth.
Oper. Res., 43(1996), 319-336..
(with B.D. Craven) A method
for establishing optimality conditions for a nonsmooth vector-valued problem,
J.Optim. Theory Appl., 95(1997), No2, 295-304.
(with B. D. Craven) Optimization
with set-functions described by functions. Optimization, 42(1997),
39-50.
(with B. D. Craven) Lagrangian
conditions for a nonsmooth vector-valued minimax, J. Austral. Math. Soc.
(Series A), 65(1998), 163-175..
General Topology, Science
and Technics Publishing House, Hanoi, 1998, 160p. (in Vietnamese).
Functional Analysis,
Science and Technics Publishing House, Hanoi, 1999, 278p. (in Vietnamese).
Lipschitz Analysis, Science
and Technics Publishing House, Hanoi, 1999, 162p. (in Vietnamese).
The theory of optimality
conditions, Science and Technics Publishing House, Hanoi, 1999, 186p.
(in Vietnamese).
(with B.D. Craven) Perturbing
convex multiobjective programs, Optimization, 48(2000), 391-407.
(with N. X. Ha) An invariant
property of invex functions and applications, Acta Math. Vietnam., 25(2000),
No2, 181-193.
(with P. T. Kien) Sufficient
optimality conditions under invexity hypotheses, Vietnam J. of Math.,
28:3(2000), 227-236.
(with P. H. Khai) Convex
Analysis, Science and Technics Publishing House, Hanoi, 2000, 236p.
(in Vietnamese).
(with D. N . Quynh) On
the Lagrangian conditions for a nonsmooth minimax, Nonl. Funct. Anal.
and Appl., 6(2001), No2, 157-169.
(with L. M. Tung) Nonsmooth
B-preinevex functions, Acta Math.Vietnam., 27 (2002) No1, 1-8.
(with N. X. Ha) Invexity
of supremum and infimum functions, Bull. Austral. Math. Soc., 65(2002)
289-306.
(with D. Hoa) On
the stability of local minima in nonsmooth mathematical programs, East-West
Journal of Mathematics 4(2002), No1, 1-12.
(with P. T. Kien)
Optimality conditions in terms of directional derivatives,
East-West Journal of Mathematics, 4(2002), No2, 119-136.
(with N. X. Ha) Sufficient
conditions for invexity, Bull. Austral. Math. Soc. 68(2003), 113 - 125.
(with P. T. Kien)
Higher-order optimality conditions for isolated local minima,
Nonlinear Funct. Anal. & Appl. 8(2003), No1, 35 – 48.
(with L.M. Tung) B-preinvexity criteria and applications,
Indian Journal of Mathematics 45 (2003) No3, 279-300
(with N.M. Hung) Invexity of constraint maps in mathematical
programs, Nonlinear Functional Analysis and Applications 9 (2004) No2,
289-304.
(with D. Hoa) On the stability of local minima in mathematical
programming involving cone-constraints, Soochow J. of Mathematics 31
(2005), No2, 273-289.
(with P. X. Trung) Theorems of the alternative for inequality-equality
systems and optimality conditions, Nonlinear Funct. Anal. Appl. 11(2006), No1, 21-35.
(with P. T. Kien) On higher-order conditions for strict efficiency, Soochow Journal of Mathematics 33(2007), No 1, 17-31.
(with N. M. Hung) On necessary conditions for efficiency in directionally differentiable optimization problems, Nonlinear
Functional Analysis and Applications 12(2007), No 3, 439-453.
Higher-order necessary and sufficient conditions for strict local Pareto minima in terms of Studniarski's derivatives, Optimization
57(2008), No 4, 593-605.
(with N. M. Hung) On alternative theorems and necessary conditions for efficiency, Optimization 58(2009), 49-62.
On constraint qualifications and optimality conditions in locally Lipschitz multiobjective programming problems, Nonl. Funct. Anal. Appl.
14(2009), 81-97.
Higher-order optimality conditions in nonsmooth cone-constrained
multiobjective programming, Nonl. Funct. Anal. Appl., vol 15(2010) No
3, 381-393.
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| Current Teaching
Functional Analysis
Convex Analysis
Lipschitz Analysis
Theory of optimality conditions
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