Le Dung Muu


Full Professor, Doctor of Science

Department of Optimization and Control Theory
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 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.
2Pham Ky Anh, Tran Viet Anh, Le Dung Muu, On Bilevel Split Pseudomonotone Variational Inequality Problems with Applications, Acta Mathematica Vietnamica, 42 (2017), 413–429.
3Dang 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.
4Phung Minh Duc , Le Dung Muu, A splitting algorithm for a class of bilevel equilibrium problems involving nonexpansive mappings, Optimization, 65 (2016), 1855-1866.
5Le 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.
6Phung Minh Duc, Le Dung Muu, Nguyen Van Quy, Solution-Existence and Algorithms with Their Convergence Rate for Strongly Pseudomonotone Equilibrium Problems, Pacific Journal of Optimization12 (2016), 833-845.
7Dang 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.
8Tran 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.
9Le 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.
10Bui 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.
11Nguyen Kieu Linh, Le Dung Muu, A convex hull algorithm for solving a location problem. RAIRO - Operations Research 49 (2015), 589–600.
12Le Dung Muu, Nguyen Van Quy, On Existence and Solution Methods for Strongly Pseudomonotone Equilibrium Problems, Vietnam Journal of Mathematics, 43(2015), 229-238.
13Le Dung Muu, Le Quang Thuy, DC optimization algorithms for solving mimax flow problems, Mathematical Methods of Operations Research, 80 (2014), 83-97.
14Bui Van Dinh, Pham Gia Hung, Le Dung Muu, Bilevel optimization as a regularization approach to pseudomonotone equilibrium problems. Numer. Funct. Anal. Optim. 35 (2014), 539–563.
15P. N. Anh, Le Dung Muu, A hybrid subgradient algorithm for nonexpansive mappings and equilibrium problems, Optim. Lett. 8 (2014), 727–738.
16Le Dung Muu, Bui Van Dinh, Algorithms for a class of bilevel programs involving pseudomonotone variational inequalities, Acta Mathematica Vietnamica 38 (2013), 529 - 540.
17Le 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.
18Le 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 Math. Viet., 37 (2012), 201 -- 217.
19Le Dung Muu, Bui Van Dinh, On Penalty and gap function methods for bilevel pseudomonotone equilibrium problems,  Journal of Applied Mathematics, 2011 (2011), 14p.
20Le Dung Muu, Tran D. Quoc and Pham N. Anh, Dual extragradient algorithms extendeded to equilibrium problems,  J. Glob. Optim., 52 (2012), 139 -- 159.
21Tran D. Quoc, Le Dung Muu, Iterative methods for solving equilibrium problems via dual gap function,  Computtational Optimization and Applications, 51 (2012), 709 -- 728.
22Le Dung Muu, Pham N. Anh and J. Kim, An extragradient algorithm for solving pseudomonotone variational inequalities,  J. Glob. Optim., 52 (2012), 252 -- 269.
23Le 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 Math.  39 (2011), 31 - 48.
24Le Dung Muu, P. G. Hung, The Tikhonov regularization extended to equilibrium problems involving pseudomonotone bifunctions,  Nonlinear Analyzis: Theory, Methods & Applications, 74 (2011), 6121 - 6129.
25Le Dung Muu, Tran Dinh Quoc, A splitting proximal method Nash-Cournot equilibrium models involving nonconvex cost functions,  Journal of Nonlinear and Convex Analysis 12, 501 -- 519.
26Le Dung Muu, D. X. Luong, Combining the projection method and the penalty function to solve the variational inequalities with monotone mappings, J. Optim. Theory Appl., 147 (2010), 124 -- 137.
27Le Dung Muu, T. D. Quoc, One step from DC optimization to DC mixed variational inequalities,Optimization, 59 (2010), 63 -- 76.
28Le 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.
29Le 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.
30Le 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.
31Le 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.
32T. D. Quoc, Le Dung Muu, and N. V. Hien, Extragradient algorithms extended to equilibrium problems, Optimization 57 (2008), 749 - 776.
33Le 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.
34Pham 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.
35Pham 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.
36 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.
37Pham 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.
38Tran Dinh Quoc, Le Dung Muu, Implementable quadratic regularization methods for solving pseudomonotone equilibrium problems. East-West J. Math. 6 (2004), 101–123.
39Pham 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.
40H.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.
41Le Dung Muu, Nguyen Van Quy, A global optimization method for solving convex quadratic bilevel programming problems, J. Global Optim. 26 (2003), 199 - 219.
42Le 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.
43Le Dung Muu, Nguyen Van Quy, Methods for finding global optimal solutions to linear programs with equilibrium constraintsVietnam J. Math. 30 (2002), 189 - 194.
44Nguyen Thi Bach Kim, Le Dung Muu, On the projection of the efficient set and potential applications, Optimization 51 (2002), 401 - 421.
45Nguyen Van Quy, Le Dung Muu, On penalty function method for a class of nonconvex constrained optimization problems. Vietnam J. Math. 29 (2001), 235 - 256.
46Le 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.
47Le 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.
48Hoang 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.
49Le Dung Muu, On the construction of initial polyhedral convex set for optimization problems over the efficient set and bilevel linear programsVietnam J. Math. 28 (2000), 177 - 182.
50J. 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.
51Le Dung Muu, A convex-concave programming method for optimizing over the efficient set. Acta Math. Vietnam. 25 (2000), 67 - 85.
52Le Thi Hoai An, Pham Dinh Tao, Le Dung Muu, Exact penalty in DC programming. Vietnam J. Math. 27 (1999), 169 - 178.
53Le 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.
54Le 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.
55Le Dung Muu, N. V. Tien, A relaxation algorithm for solving mixed integer programming problems. Acta Math. Vietnam. 22 (1997), 367 - 378.
56Le Dung Muu, Le Tu Luc, On equivalence between convex maximization and optimization over the efficient set. Vietnam J. Math. 24 (1996), 439 - 445.
57Le 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.
58Nguyen 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.
59Nguyen 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.
60Le Dung Muu, Computational aspects of optimization over the efficient set. Vietnam J. Math. 23 (1995), 85 - 106.
61Le 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.
62Le 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.
63Le Dung Muu, Bui The Tam, Efficient methods for solving certain bilinear programming problems. Acta Math. Vietnam. 19(1994), 97 - 110.
64R. Horst, Le Dung Muu, M. Nast, Branch-and-bound decomposition approach for solving quasiconvex-concave programs. J. Optim. Theory Appl. 82 (1994), 267 - 293.
65Le Dung Muu, Convex-concave programming as a decomposition approach to global optimization. Acta Math. Vietnam. 18 (1993), 61 - 77.
66W. 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.
67Le Dung Muu, An algorithm for solving convex programs with an additional convex-concave constraint. Math. Programming 61 (1993), 75 - 87.
68Le 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.
69Le 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.
70Le Dung Muu, On a Lagrangian penalty function method for convex programs. Appl. Math. Optim. 25 (1992), 1 - 9.
71Le Dung Muu, W. Oettli, An algorithm for indefinite quadratic programming with convex constraints. Operations Resarch Letters 10 (1991), 323 - 327.
72Le Dung Muu, W. Oettli, A method for minimizing a convex-concave function over a convex set. J. Optim. Theory Appl. 70 (1990), 377 - 384.
73Le Dung Muu, W. Oettli, A Lagrangian penalty function method for monotone variational inequalities. Numer. Funct. Anal. Optim. 10 (1989), 1003 - 1017.
74Le Dung Muu, An augmented penalty function method for solving a class of variational inequalities. Soviet Computational Mathematics and Mathematical Physics 12 (1986), 1788 - 1796.
75Le Dung Muu, A convergent algorithm for solving linear programs with an additional reverse convex constraint. Kybernetika 91 (1986), 418 - 425 (in Russian).
76Le Dung Muu, Stability property of a class of variational inequalities. Optimization 15 (1984), 347 - 351.
77Le Dung Muu, Do Ba Khang, Asymtotic regularity and the strong convergence of the proximal point algorithm. Acta Math. Vietnam. 8 (1983), 3 - 11 (1984).
78Hoang Tuy, N. V. Thoai, Le Dung Muu, A modification of Scarf's algorithm allowing restarting, Math. Oper. Stati. Ser. Optim. 9 (1978), 357 - 372.
79Hoang 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