Le Dung Muu
Full Professor, Doctor of Science

Cộng tác viên
Research interests: Methods for equilibrium problems including variational inequalities, complementarity problems, optimization problems


Address
Office: Building A5, Room 210
Tel: +84 (0)4 37563474/210
Email: ldmuu AT math.ac.vn

Born in Thanh Hoa in 1949

Education and academic degrees

  • Bachelor 1972 /Master: 1973, University of Budapest. Hungary 
  • Doctor of Science 1996, Institute of Mathematics. VAST
  • Full Professor 2003
  • Researcher


Research areas: Optimization, Variational Inequality, Equilibrium Problems

 PUBLICATIONS

List of publications in MathSciNet

 

List of recent publications
1Le Dung Muu, Le Xuan Thanh, Nguyen Ngoc Hai , On the proximal mapping for multi-valued monotone variational inequality problems, Optimization Letters volume 17, pages 369–383 (2023), (SCI-E, Scopus).
2Le Hai Yen, Le Dung Muu, A parallel subgradient projection algorithm for quasiconvex equilibrium problems under the intersection of convex sets. Optimization 71 (2022), no. 15, 4447–4462, (SCI-E, Scopus).
3Le Dung Muu, Le Xuan Thanh, On fixed point approach to equilibrium problem, Journal of Fixed Point Theory and Applications, 23 (2021), Article number: 50, (SCI-E, Scopus, Preprint: download here).
4Le Hai Yen, Le Dung Muu, A normal-subgradient algorithm for fixed point problems and quasiconvex equilibrium problems, Applied Set-Valued Analysis and Optimization, 2 (2020), No. 3, pp. 329-337.
5Le Dung Muu, Nguyễn Văn Quý, Global Optimization fromConcave Minimization to Concave Mixed Variational Inequality, Acta Mathematica Vietnamica 45 (2020), 449-462, Scopus.
6Le Hai Yen, Le Dung Muu, A subgradient method for equilibrium problems involving quasiconvex bifunctions, Operations Research Letter 48 (2020), 579-583, SCI-E, Scopus.
7Dang Van Hieu, Jean Jacques Strodiot, Le Dung Muu, An Explicit Extragradient Algorithm for Solving Variational Inequalities, Journal of Optimization Theory and Applications volume 185 (2020), 476–503, SCI(-E), Scopus.
8Le Hai Yen, Nguyen Thi Thanh Huyen, Le Dung Muu, Muu, Le Dung A subgradient algorithm for a class of nonlinear split feasibility problems: application to jointly constrained Nash equilibrium models. Journal of Global Optimization 73 (2019), 849–868, SCI(-E); Scopus.
9Dang Van Hieu, Dang Xuan Son, Pham Ky Anh, Le Dung Muu, A Two-Step Extragradient-Viscosity Method for Variational Inequalities and Fixed Point Problems, Acta Mathematica Vietnamica, 44 (2019), pp 531–552, Scopus.
10Le Dung Muu, Le Xuan Thanh, A splitting algorithm for finding fixed points of nonexpansive mappings and solving equilibrium problems. Journal of Fixed Point Theory and Applications, 20:130, 2018, SCI(-E); Scopus.
11Le Quang Thuy, Pham Ky Anh, Le Dung Muu, Trinh Ngoc Hai, Novel Hybrid Methods for Pseudomonotone Equilibrium Problems and Common Fixed Point Problems, Numerical Functional Analysis and Optimization, 38 (2017), 443–465,SCI(-E); Scopus.
12Pham Ky Anh, Tran Viet Anh, Le Dung Muu, On Bilevel Split Pseudomonotone Variational Inequality Problems with Applications, Acta Mathematica Vietnamica, 42 (2017), 413–429, Scopus.
13Dang Van Hieu, Pham Ky Anh, Le Dung Muu, Modified hybrid projection methods for finding common solutions to variational inequality problems, Computational Optimization and Applications, 66 (2017), 75–96, SCI(-E); Scopus.
14Phung Minh Duc , Le Dung Muu, A splitting algorithm for a class of bilevel equilibrium problems involving nonexpansive mappings, Optimization, 65 (2016), 1855-1866, SCI(-E); Scopus.
15Le Hai Yen, Le Dung Muu, Nguyen Thi Thanh Huyen, An algorithm for a class of split feasibility problems: application to a model in electricity production, Mathematical Methods of Operations Research, 84, (2016), 549-565, SCI(-E); Scopus.
16Phung Minh Duc, Le Dung Muu, Nguyen Van Quy, Solution-Existence and Algorithms with Their Convergence Rate for Strongly Pseudomonotone Equilibrium Problems, Pacific Journal of Optimization 12 (2016), 833-845, SCI(-E); Scopus.
17Dang Van Hieu, Le Dung Muu, Pham Ky Anh, Parallel hybrid extragradient methods for pseudomonotone equilibrium problems and nonexpansive mappings, Numerical Algorithms, 73 (2016), 197-217,SCI(-E); Scopus.
18Tran Viet Anh, Le Dung Muu, A projection-fixed point method for a class of bilevel variational inequalities with split fixed point constraints. Optimization 65 (2016), 1229–1243,SCI(-E); Scopus.
19Le Quang Thuy, Le Dung Muu, A Hybrid method for a system involving equilibrium problems, variational inequalitíes and nonexpansive semigroup, Journal of the Korean Mathematical Society, 28 (2015), 457-478,SCI(-E); Scopus.
20Bui Van Dinh, Le Dung Muu, A projection algorithm for solving pseudomonotone equilibrium problems and its application to a class of bilevel equilibria, Optimization 64 (2015), 559–575, SCI(-E); Scopus.
21Nguyen Kieu Linh, Le Dung Muu, A convex hull algorithm for solving a location problem. RAIRO - Operations Research 49 (2015), 589–600, SCI(-E), Scopus.
22Le Dung Muu, Nguyen Van Quy, On Existence and Solution Methods for Strongly Pseudomonotone Equilibrium Problems, Vietnam Journal of Mathematics, 43(2015), 229-238,Scopus.
23Le Dung Muu, Le Quang Thuy, DC optimization algorithms for solving mimax flow problems, Mathematical Methods of Operations Research, 80 (2014), 83-97, SCI(-E), Scopus.
24Bui Van Dinh, Pham Gia Hung, Le Dung Muu, Bilevel optimization as a regularization approach to pseudomonotone equilibrium problems. Numerical Functional Analysis and Optimization 35 (2014), 539–563, SCI(-E), Scopus.
25P. N. Anh, Le Dung Muu, A hybrid subgradient algorithm for nonexpansive mappings and equilibrium problems, Optimization Letters 8 (2014), 727–738, SCI(-E); Scopus.
26Le Dung Muu, Bui Van Dinh, Algorithms for a class of bilevel programs involving pseudomonotone variational inequalities, Acta Mathematica Vietnamica 38 (2013), 529 - 540.
27Le Dung Muu, Pham Gia Hung, On  inexact Tikhonov and proximal point regularization methods for solving pseudomonotone equilibrium problems,  Vietnam Journal of Mathematics,  40 (2012), 255 -- 274, Scopus.
28Le Dung Muu, Q. Tran Dinh, L. T. H. An and P. D. Tao, A New decomposition algorithms for globally solving mathematical programs with affine equilibrium constraints,  Acta Mathematica Vietnamica, 37 (2012), 201 -- 217, Scopus.
29Le Dung Muu, Tran D. Quoc and Pham N. Anh, Dual extragradient algorithms extendeded to equilibrium problems,  Journal of Global Optimization, 52 (2012), 139 -- 159, SCI(-E); Scopus.
30Tran D. Quoc, Le Dung Muu, Iterative methods for solving equilibrium problems via dual gap function,  Computtational Optimization and Applications, 51 (2012), 709 -- 728, SCI(-E); Scopus.
31Le Dung Muu, Pham N. Anh and J. Kim, An extragradient algorithm for solving bilevel pseudomonotone variational inequalities; Journal of Global Optimization, 52 (2012), pp 627–639, SCI(-E); Scopus.
32Le Dung Muu, L. Q. Thuy, Smooth optimization algorithms for optimizing over the Pareto efficient set and their application to minmax flow problem,  Vietnam Journal of Mathematics 39 (2011), 31 - 48, Scopus.
33Le Dung Muu, P. G. Hung, The Tikhonov regularization extended to equilibrium problems involving pseudomonotone bifunctions,  Nonlinear Analyzis: Theory, Methods & Applications, 74 (2011), 6121 - 6129, SCI(-E); Scopus.
34Le Dung Muu, Tran Dinh Quoc, A splitting proximal method Nash-Cournot equilibrium models involving nonconvex cost functions, Journal of Nonlinear and Convex Analysis12, 501 -- 519, SCI(-E); Scopus.
35Le Dung Muu, Bui Van Dinh, On Penalty and gap function methods for bilevel pseudomonotone equilibrium problems,  Journal of Applied Mathematics, 2011 (2011), 14p, Scopus.
36Le Dung Muu, D. X. Luong, Combining the projection method and the penalty function to solve the variational inequalities with monotone mappings, International Journal of Optimization. Theory Methods and Applications, 2 (2010), 124–137.
37Le Dung Muu, T. D. Quoc, One step from DC optimization to DC mixed variational inequalities, Optimization, 59 (2010), 63 -- 76, SCI(-E); Scopus.
38Le Dung Muu, L. T. H. An, P. D. Tao and N. C. Nam), Methods for optimization over the efficient and weakly efficient sets of an affine fractional vector optimization program, Optimization, 59 (2010), 77 -- 93, SCI(-E); Scopus.
39Le Dung Muu, T. D. Quoc, Regularization algorithms for solving monotone Ky Fan inequalities with application to a Nash-Cournot equilibria model, J. Optimization Theory and Application, 142 (2009), 185-204.
40Le Dung Muu, P.N.Anh and J-J. Strodiot, Generalized projection method for non-Lipschitz multivalued monotone variational inequalities, Acta Math. Vietnamica, 34 (2009), 67-80.
41Le Dung Muu, N. V. Hien and N. V. Quy, On Nash-Cournot oligopolistic market equilibrium models with concave cost functions, J. Global Optim. 41 (2008), 351 - 364.
42T. D. Quoc, Le Dung Muu, and N. V. Hien, Extragradient algorithms extended to equilibrium problems, Optimization 57 (2008), 749 - 776.
43Le Dung Muu, Nguyen Van Quy, On branch-and-bound algorithms for global optimal solutions to mathematical programs with affine equilibrium constraints, Vietnam J. Math. 35 (2007),  523 - 539.
44Pham Ngoc Anh, Le Dung Muu, Contraction mapping fixed point algorithms for solving multivalued mixed variational inequalities,  Optimization with multivalued mappings, 231 - 249, Springer Optim. Appl. 2, Springer, New York, 2006.
45Pham Ngoc Anh, Le Dung Muu, Lagrangian duality algorithms for finding a global optimal solution to mathematical programs with affine equilibrium constraints, Nonlinear Dyn. Syst. Theory 6 (2006), N0 3, 225 - 244.
46 P. N. Anh, Le Dung Muu, V. H. Nguyen, J. J. Strodiot, Using the Banach contraction principle to implement the proximal point method for multivalued monotone variational inequalities. J. Optim. Theory Appl. 124 (2005),  285–306.
47Pham Ngoc Anh, Le Dung Muu, Van Hien Nguyen, Jean-Jacques Strodiot, On the contraction and nonexpansiveness properties of the marginal mappings in generalized variational inequalities involving co-coercive operators. In: Generalized convexity, generalized monotonicity and applications, 89-111, Nonconvex Optim. Appl. 77, Springer, New York, 2005.
48Tran Dinh Quoc, Le Dung Muu, Implementable quadratic regularization methods for solving pseudomonotone equilibrium problems. East-West J. Math. 6 (2004), 101–123.
49Pham Ngoc Anh, Le Dung Muu, Coupling the Banach contraction mapping principle and the proximal point algorithm for solving monotone variational inequalities,Acta Math. Vietnam. 29 (2004), 119 - 133.
50H.A. Le Thi, T. Pham Dinh, Le Dung Muu, Simplicially-constrained DC optimization over efficient and weakly efficient sets, J. Optim. Theory Appl. 117 (2003), 503 - 531.
51Le Dung Muu, Nguyen Van Quy, A global optimization method for solving convex quadratic bilevel programming problems, J. Global Optim. 26 (2003), 199 - 219.
52Le Dung Muu, Hoang Quang Tuyen, Bilinear programming approach to optimization over the efficient set of a vector affine fractional problem, Acta Math. Vietnam. 27 (2002), 119 - 139.
53Le Dung Muu, Nguyen Van Quy, Methods for finding global optimal solutions to linear programs with equilibrium constraints, Vietnam J. Math. 30 (2002), 189 - 194.
54Nguyen Thi Bach Kim, Le Dung Muu, On the projection of the efficient set and potential applications, Optimization 51 (2002), 401 - 421.
55Nguyen Van Quy, Le Dung Muu, On penalty function method for a class of nonconvex constrained optimization problems. Vietnam J. Math. 29 (2001), 235 - 256.
56Le Dung Muu, Nguyen Van Quy, Methods for finding global optimal solutions to linear programs with equilibrium constraints. Dedicated to Pham Huu Sach on the occasion of his sixtieth birthday. Acta Math. Vietnam. 26 (2001), 333 - 347.
57Le Dung Muu, Werner. Oettli, Optimization over equilibrium sets. In celebration of Prof. Dr. Alfred Gopfert 65th birthday. Optimization 49 (2001), N0 1-2, 179 - 189.
58Hoang Q. Tuyen, Le Dung Muu, Biconvex programming approach to optimization over the weakly efficient set of a multiple objective affine fractional problem. Oper. Res. Lett. 28 (2001), 81 - 92.
59Le Dung Muu, On the construction of initial polyhedral convex set for optimization problems over the efficient set and bilevel linear programs, Vietnam J. Math. 28 (2000), 177 - 182.
60J. Fülöp, Le Dung Muu, Branch-and-bound variant of an outcome-based algorithm for optimizing over the efficient set of a bicriteria linear programming problem. J. Optim. Theory Appl. 105 (2000), 37 - 54.
61Le Dung Muu, A convex-concave programming method for optimizing over the efficient set. Acta Math. Vietnam. 25 (2000), 67 - 85.
62Le Thi Hoai An, Pham Dinh Tao, Le Dung Muu, Exact penalty in DC programming. Vietnam J. Math. 27 (1999), 169 - 178.
63Le Thi Hoai An, Pham Dinh Tao, Le Dung Muu, A combined D.C. optimization-ellipsoidal branch-and-bound algorithm for solving nonconvex quadratic programming problems. J. Comb. Optim. 2 (1998), 9 - 28.
64Le Tu Luc, Le Dung Muu, Global optimization approach to optimization over the efficient set. In: the Proceeding of 8th French-German Conference on Optimization. Springer Verlag, Berlin, 1997, 213 - 221.
65Le Dung Muu, N. V. Tien, A relaxation algorithm for solving mixed integer programming problems. Acta Math. Vietnam. 22 (1997), 367 - 378.
66Le Dung Muu, Le Tu Luc, On equivalence between convex maximization and optimization over the efficient set. Vietnam J. Math. 24 (1996), 439 - 445.
67Le Thi Hoai An, Pham Dinh Tao, Le Dung Muu, Numerical solution for optimization over the efficient set by D. C. optimization algorithm. Operations Research Letters 19 (1996), 117 - 128.
68Nguyen Dinh Dan, Le Dung Muu, Parametric simplex method for optimizing a linear function over the efficient set of a bicriteria linear problem. Acta Math. Vietnam. 21 (1996), 59 - 67.
69Nguyen Anh Tuan, Le Dung Muu, Pham Canh Duong, A decomposition method for finding a global optimal solution to a water distribution network. Acta Math. Vietnam. 21 (1996), 309 - 333.
70Le Dung Muu, Computational aspects of optimization over the efficient set. Vietnam J. Math. 23 (1995), 85 - 106.
71Le Dung Muu, Thai Quynh Phong, Pham Dinh Tao, Decomposition methods for solving a class of nonconvex programming problems dealing with bilinear and quadratic function. Comput. Optim. Appl. 4 (1995), 203 - 216.
72Le Dung Muu, Bui The Tam, S. Schaible, Efficient algorithms for solving certain nonconvex optimization problems dealing with the product of two affine fractional functions. J. Global Optim. 6 (1995), 179 - 191.
73Le Dung Muu, Bui The Tam, Efficient methods for solving certain bilinear programming problems. Acta Math. Vietnam. 19(1994), 97 - 110.
74R. Horst, Le Dung Muu, M. Nast, Branch-and-bound decomposition approach for solving quasiconvex-concave programs. J. Optim. Theory Appl. 82 (1994), 267 - 293.
75Le Dung Muu, Convex-concave programming as a decomposition approach to global optimization. Acta Math. Vietnam. 18 (1993), 61 - 77.
76W. Oettli, Le Dung Muu, Combimed branch-and-bound and cutting plane method for solving a certain class of nonconvex optimization problems. J. Global Optim. 3 (1993), 377 - 391.
77Le Dung Muu, An algorithm for solving convex programs with an additional convex-concave constraint. Math. Programming 61 (1993), 75 - 87.
78Le Dung Muu, Bui The Tam, Minimizing the sum of a convex function and the product of two affine functions over a convex set. Optimization 24 (1992), 57 - 62.
79Le Dung Muu, W. Oettli, Convergence of an adaptive penalty method for monotone variational inequalities and convex optimization. Nonlinear Analysis: Theory, Methods and Applications 18 (1992), 1159 - 1166.
80Le Dung Muu, On a Lagrangian penalty function method for convex programs. Appl. Math. Optim. 25 (1992), 1 - 9.
81Le Dung Muu, W. Oettli, An algorithm for indefinite quadratic programming with convex constraints. Operations Resarch Letters 10 (1991), 323 - 327.
82Le Dung Muu, W. Oettli, A method for minimizing a convex-concave function over a convex set. J. Optim. Theory Appl. 70 (1990), 377 - 384.
83Le Dung Muu, W. Oettli, A Lagrangian penalty function method for monotone variational inequalities. Numer. Funct. Anal. Optim. 10 (1989), 1003 - 1017.
84Le Dung Muu, An augmented penalty function method for solving a class of variational inequalities. Soviet Computational Mathematics and Mathematical Physics 12 (1986), 1788 - 1796.
85Le Dung Muu, A convergent algorithm for solving linear programs with an additional reverse convex constraint. Kybernetika 91 (1986), 418 - 425 (in Russian).
86Le Dung Muu, Stability property of a class of variational inequalities. Optimization 15 (1984), 347 - 351.
87Le Dung Muu, Do Ba Khang, Asymtotic regularity and the strong convergence of the proximal point algorithm. Acta Math. Vietnam. 8 (1983), 3 - 11 (1984).
88Hoang Tuy, N. V. Thoai, Le Dung Muu, A modification of Scarf's algorithm allowing restarting, Math. Oper. Stati. Ser. Optim. 9 (1978), 357 - 372.
89Hoang Tuy, N. V. Thoai, Le Dung Muu, Un nouvel algorithme de point fixe. C. R. Acad. Sci. Paris 286 (1978), Ser. A, 783 - 785.
Preprints
1IMH20170903, Le Dung Muu, Nguyen Van Quy, Algorithms for finding global and local equilibrium points of Nash-Cournot equilibrium models involving concave cost.
2IMH20161203, P.T. Hoai, Le Dung Muu, T.N. Thang, Finding the Edgeworth-Pareto hull and its application to optimization over the efficient set of multiple objective discrete linear programs
3IMH2014/02/01, Le Dung Muu, Nguyen Van Quy, On Equilibrium Problems Involving, Strongly Pseudomonotone Bifunctions