Publications

Google Scholars

BOOKS

1.  B. Mordukhovich, Nguyen Mau Nam: An Easy Path to Convex Analysis and Applications (Second Edition), Synthesis Lectures on Mathematics and Statistics, Springer, Cham, Switzerland, 2023. 

2.  B. Mordukhovich, Nguyen Mau Nam: Convex Analysis and Beyond,  Vol. 1: Basic Theory,   XII+585 pp.,  Springer, Cham, Switzerland, 2022.

3.  B. Mordukhovich, Nguyen Mau Nam: An Easy Path to Convex Analysis and Applications, Synthesis Lectures on Mathematics and Statistics (with Chinese and Farsi translations), Morgan & Claypool Publishers, 2014.

4.   B. Lafferiere, G. Lafferiere, Nguyen Mau Nam, Introduction to Mathematical Analysis I, PDX Open: Reducing Student Textbook Costs (First Edition: 2014; Second Edition: 2016).

RESEARCH ARTICLES

1. 1. 1.  N.N. Luan, Nguyen Mau Nam, N.D. Yen, Properties of generalized polyhedral convex multifunctions, to appear in Optimization (2024).

      2. Nguyen Mau Nam, G. Sandine, N.N. Thieu, N.D. Yen, Near convexity and generalized differentiation, to appear in  Journal of Convex Analysis (2024).

      3. Nguyen Mau Nam, G. Sandine, N.N. Thieu, N.D. Yen, A Notion of Fenchel conjugate for set-Valued mappings, to appear in  Journal of Optimization Theory and Applications (2024).

      4. N.N. Luan, Nguyen Mau Nam, N.N. Thieu, N.D. Yen, Relationships between polyhedral convex sets and generalized polyhedral convex sets, Journal of Optimization Theory and Applications 199 (2023), 766–786.

      5. D.V. Cuong, B. Mordukhovich, Nguyen Mau Nam, G. Sandine, Fenchel-Rockafellar theorem in infinite dimensions via generalized interiors, Journal of Convex Analysis 30 (2023), 835–850.

      6.  D.V. Cuong, B. Mordukhovich, Nguyen Mau Nam, N. M. Nam, G. Sandine, Generalized differentiation and duality in infinite dimensions under polyhedral convexity, Set-Valued and Variational Analysis  30 (2022) , 1503–1526.

      7.  D.V. Cuong, B. Mordukhovich, Nguyen Mau Nam, M. Wells, Convex analysis of minimal time and signed minimal time functions, Optimization 71 (2022), 849–876.

      8.  A. Bajaj, B. Mordukhovich, Nguyen Mau Nam, T. Tran, Solving a continuous multifacility location problem by DC algorithms, Optimization Methods and Software 37 (2022), 338–360.

      9.  D.V. Cuong, B. Mordukhovich, Nguyen Mau Nam, A. Cartmell, Algebraic core and convex calculus without topology, Optimization 71 (2022), 309–335. 

      10.   D.V. Cuong, B. Mordukhovich, Nguyen Mau Nam,  Extremal systems of convex sets with applications to convex calculus in vector spaces, Pure Applied Functional Analysis 6  (2021), 1139-1155.

      11.  D.V. Cuong, B. Mordukhovich, Nguyen Mau Nam, Quasi-relative interiors for graphs of convex set-valued mappings, Optimization Letters 15 (2021), 933–952.

      12.  N.T. An, Nguyen Mau Nam, X, Qin, Solving k-center problems involving sets based on optimization techniques. Journal of Global Optimization 76 (2020), 189–209. 

      13.  B. Mordukhovich, Nguyen Mau Nam, The Fermat-Torricelli problem and Weiszfeld algorithm in the light of convex analysis. Journal of Applied and Numerical Optimization 1 (2019), 205–215.

      14. Nguyen Mau Nam, H. Phan, B. Wang. Bornological coderivative and subdifferential calculus in smooth Banach spaces. Set-Valued and Variational Analysis 27 (2019), 971–993.

      15.  Nguyen Mau Nam, L.T.H. An, D. Giles, N.T. An. Smoothing techniques and difference of convex functions algorithms for image reconstructions. Optimization 69 (2019), 1601–1633. 

      16.  Nguyen Mau Nam, D.V. Cuong, Subgradients of minimal time functions without calmness, Journal of Convex Analysis 26 (2019), 189–200.

      17.  W. Geremew, Nguyen Mau Nam, A. Semenov, V. Boginski, E. Pasiliao, A DC programming approach for solving multicast network design    problems via the Nesterov smoothing technique, Journal of Global Optimization 72 (2018), 705–729.

      18.   Nguyen Mau Nam, N. T. An, S. Reynolds, T. Tran, Clustering and multifacility location with constraints via distance function penalty methods and DC programming, Optimization 67 (2018), 1869–1894.

      19.  Nguyen Mau Nam, W. Geremew, S. Reynolds, T. Tran, The Nesterov smoothing technique and minimizing differences of convex functions for hierarchical clustering, Optimization Letters 12 (2018), 455–473.

      20.  Nguyen Mau Nam, R.B. Rector, D. Giles, Minimizing differences of convex functions with applications to facility location and clustering, Journal of Optimization Theory and Applications 173 (2017), 255-278.

      21.  B. Mordukhovich, Nguyen Mau Nam, R.B. Rector, T. Tran, Variational geometric approach to generalized differential and conjugate calculus in convex analysis, Set-Valued and Variational Analysis 25 (2017), 731–755. 

      22.  B. Mordukhovich, Nguyen Mau Nam, Extremality of convex sets with some applications, Optimization Letters 11 (2017), 1201–1215.

      23.  N.T. An, Nguyen Mau Nam, Convergence analysis of a proximal point algorithm for minimizing differences of functions, Optimization 66 (2017), 129-147.

      24.  B. Mordukhovich, Nguyen Mau Nam, Geometric approach to subdifferential calculus, Optimization 66 (2017), 839-873.

      25.  N.T. An, D. Giles, Nguyen Mau Nam, R.B. Rector, The log-exponential smoothing technique and Nesterov accelerated gradient method for generalized Sylvester problems,  Journal of Optimization Theory and Applications 168 (2016), 559–583.'

      26.  N. T. An, Nguyen Mau Nam, N.D. Yen, A DC algorithm via convex analysis approach for solving a location problem involving sets, Journal of Convex Analysis 23 (2016), 077-101.

      27.  Nguyen Mau Nam, Subgradients for a class of nonconvex infimal convolutions, Optimization 64 (2015), 2213-2222.

      28.  Nguyen Mau Nam, D.V. Cuong, Generalized differentiation and characterizations for differentiability of infimal convolutions,  Journal of Set-Valued and Variational Analysis 23 (2015), 333-353.

      29.  S.S. Akmal, Nguyen Mau Nam, J.J.P Veerman, On a convex set with nondifferentiable metric projection, Optimization Letters 9 (2015), 1039-1052.

      30.  H. Martini, Nguyen Mau Nam, A. Robinson, On the equivalence of the theorems of  Helly, Radon, and Carathéodory via convex analysis, Journal of Convex Analysis 22 (2015), 591-601.

      31.  Nguyen Mau Nam, N.T. An, R.B. Rector, J. Sun, Nonsmooth algorithms and Nesterov smoothing techniques for generalized Fermat-Torricelli problems, SIAM Journal on Optimization 24 (2014), 1815-1839.

      32.  N. Hoang, Nguyen Mau Nam, Layered viscosity solutions of nonautonomous Hamilton-Jacobi equations: semiconvexity and relations to characteristics. Journal of Mathematical Analysis and Applications 410 (2014), 687–698.

      33.  Nguyen Mau Nam, N.D. Hoang, R.B. Rector, A unified approach to convex and convexified generalized differentiation of nonsmooth functions and set-valued mappings, Vietnam Journal of Mathematics  (invited paper) 42 (2014), 479-497.

      34.  B. Mordukhovich, Nguyen Mau Nam, N. Nhi,  Partial second-order subdifferentials in variational analysis and optimization, Journal of Numerical Functional Analysis and Optimization 35  (2014), 1113-1151.

      35.  Nguyen Mau Nam, N. Hoang, N.T. An, Constructions of solutions to generalized Sylvester and Fermat-Torricelli problems for Euclidean balls, Journal of Optimization Theory and Applications 160 (2014), 483-509.

      36.  Nguyen Mau Nam, G. Lafferriere, Lipchitz properties of nonsmooth functions and set-valued mappings via generalized differentiation, Nonlinear Analysis: Theory, Methods and Applications 89 (2013), 110-120.\

      37.  Nguyen Mau Nam, N. Hoang, A generalized Sylvester problem and a generalized Fermat-Torricelli problem, Journal of Convex Analysis 20 (2013), 669-687.

      38.  Nguyen Mau Nam, C. Zalinescu, Variational analysis of directional minimal time functions and applications to location problems, Journal of Set-Valued and Variational Analysis 21 (2013), 405-430.

      39.  B. Mordukhovich, Nguyen Mau Nam, C. Villalobos, The smallest enclosing ball problem and the smallest intersecting ball problem: existence and uniqueness of solutions, Optimization Letters 7 (2013), 839-853.

      40.  Nguyen Mau Nam, N.T. An, C. Villalobos, Minimal time functions and the smallest intersecting ball problem with unbounded dynamics, Journal of Optimization Theory and Applications 154 (2012), 768-791.

      41.   B. Mordukhovich, Nguyen Mau Nam, J. Salinas, Applications of variational analysis to a generalized Heron problem, Applicable Analysis 91 (2012), 1915-1942.

      42.  Nguyen Mau Nam, B. Wang, Outer semicontinuity of subdifferential and normal cone mappings, Applicable Analysis 91 (2012), 2145-2168.

      43.  Nguyen Mau Nam, N.T. An, J. Salinas, Applications of convex analysis to the smallest intersecting ball problem, Journal of Convex Analysis 19 (2012), 497-518.

      44.  B. Mordukhovich, Nguyen Mau Nam, H. Phan, Variational analysis of marginal functions with applications to bilevel programming,  Journal of Optimization Theory and Applications 152 (2012), 557-586.

      45.  B. Mordukhovich, Nguyen Mau Nam, J. Salinas, Solving a generalized Heron problem by means of convex analysis, American Math Monthly 119 (2012), 87-99.

      46.  Nguyen Mau Nam, B. Wang, Metric regularity, tangential distances, and generalized differentiation in Banach spaces, Nonlinear Analysis: Theory, Methods and Applications 75 (2012), 1496-1506.

      47.  B. Mordukhovich, Nguyen Mau Nam, Subgradients of minimal time functions under minimal requirements, Journal of Convex Analysis 18 (2011), 915-947.

      48.  B. Mordukhovich, Nguyen Mau Nam, Applications of variational analysis to a generalized Fermat - Torricelli problem, Journal of Optimization Theory and Applications 148 (2011), 431-454. 

      49.  Nguyen Mau Nam, Coderivatives of normal cone mappings and applications to Lipschitzian stability, Nonlinear Analysis: Theory, Methods and Applications 73 (2010), 2271-2282.

      50.  R. Henrion, B. Mordukhovich, Nguyen Mau Nam, Second-order analysis of polyhedron systems in finite and infinite dimensions with applications to robust stability of variational inequalities, SIAM Journal on Optimization 20 (2010), 2199-2227.

      51.  B. Mordukhovich, Nguyen Mau Nam, Limiting subgradients of minimal time functions in Banach spaces, Journal of Global Optimization 46 (2010) 615-633.

      52.  B. Mordukhovich, Nguyen Mau Nam, B. Wang, Metric regularity of mappings and generalized normals to set images, Journal of Set-Valued and Variational Analysis 17 (2009), 359-387.

      53.  B. Mordukhovich, Nguyen Mau Nam, Variational analysis of extended generalized equations via coderivative calculus in Asplund spaces, Journal of Mathematical Analysis and Applications 350 (2009), 663-679. 

      54.  W. Gemerew, B. Mordukhovich, Nguyen Mau Nam, Coderivative calculus and metric regularity for constraint and variational systems, Nonlinear Analysis: Theory, Methods and Applications 70 (2009), 529-552.

      55.  B. Mordukhovich, Nguyen Mau Nam, N.D. Yen, Subgradients of marginal functions in parametric mathematical programming, Mathematical Programming 116 (2009), 396-369.  

      56.  Nguyen Mau Nam, N.D. Yen, Relationships between approximate Jacobians and coderivatives, Journal of Nonlinear and Convex Analysis 8 (2007), 121-133.

      57.  B. Mordukhovich, Nguyen Mau Nam, Exact calculus for proximal subgradients with applications to optimization, ESAIM Proc. 17 (2007), 80-95.  

      58.  B. Mordukhovich, Nguyen Mau Nam, N.D. Yen, Fréchet subdifferential calculus and optimality conditions in nondifferentiable programming, Optimization 55 (2006), 685-708.

      59.  B. Mordukhovich, Nguyen Mau Nam, Subgradient of distance functions at out-of-set points, Taiwanese Journal of Mathematics 10 (2006), 299-326. 

      60.   B. Mordukhovich, Nguyen Mau Nam, Subgradient of distance functions with applications to Lipschitzian stability, Mathematical Programming 104 (2005), 635-668.

      61.  B. Mordukhovich, Nguyen Mau Nam, Variational stability and marginal functions via generalized differentiation, Mathematics Operation Research 30 (2005), 800-816.